Factoring The Differences Of Two Squares Examples
1. Factorize the following algebraic expressions
Given expression is 64 a2Rewrite the above expression.The above equation 82 a2;is in the form of a2; b2.Now, apply the formula of a2; b2 = , where a = 8 and b = a
The final answer is
Given expression is 3m2 27n2Rewrite the above expression. Take 3 common.3 2) where 9n2 = 2The above equation 2) ;is in the form of a2; b2.Now, apply the formula of a2; b2 = , where a = m and b = 3n 3
The final answer is 3
Given expression is a3 25aRewrite the above expression. Take a common.a The above equation 2 2);is in the form of a2; b2.2 2)Now, apply the formula of a2; b2 = , where a = a and b = 5 a
The final answer is a
2. Factor the expressions
Given expression is 81×2 2Rewrite the above expression.The above equation 2 2);is in the form of a2; b2.2 2)Now, apply the formula of a2; b2 = , where a = 9x and b = y z) )
The final answer is
Solution:Given expression is 252 362Rewrite the above expression.2 2The above equation 2 2;is in the form of a2; b2.)2 )2)Now, apply the formula of a2; b2 = , where a = 5 and b = 6
The final answer is
Solution:Given expression is 2 2The above equation 2 2;is in the form of a2; b2.2 2Now, apply the formula of a2; b2 = , where a = m 2 and b = m 3
What Does Difference Mean In Math
In mathematics the difference is the result of subtracting one number from another, and represents the operation of removing objects from a collection. Mathematicians use the term “difference,” because it shows by how much the two numbers in the subtraction problem differ.
A basic subtraction problem is made up of three parts: the minuend, the subtrahend and the difference. The minuend is the number which appears first in the problem. This is the number which is being subtracted from. The subtrahend appears second, and is the amount being subtracted from the minuend. The difference appears last, after the equals sign, and is the amount of space between the minuend and subtrahend.
If the minuend is greater than the subtrahend, then the difference is always positive. If the minuend is less than the subtrahend, then the difference is always negative. In the order of operations, differences are the last things calculated, along with sums. Therefore, parentheses are necessary to calculate a difference before an exponent, product or quotient.
For subtracting large numbers by hand, use partial differences. These rely on the subtraction of digits in certain positions, rather than the whole number. For example, a partial difference of 753 – 491 is 700 – 400.
Differences In Mathematics Motivation Between Boys And Girls
We found statistically significant differences in mathematics motivation between boys and girls in primary education, with a moderate effect size, even though the differences in mathematics performance were not significant . Girls reported lower levels of self-efficacy and intrinsic motivation for mathematics than did boys. On the other hand, whereas both boys and girls had similar levels of negative feelings toward mathematics , the girls exhibited higher rates of math anxiety than did their male classmates .
Don’t Miss: What Is Three Dimensional Geometry
Visuospatial Ability And Mathematics And Science Careers
All of the above studies speak to the power of mathematical reasoning ability in predicting subsequent math/science achievement. Yet prediction can be improved if one considers visuospatial ability and the relative strength of mathematical ability compared to verbal ability within a given individual, both of which display sex differences. Individual differences in the relative strength of verbal, mathematical, and quantitative abilities that are identified at an early age can predict differences in developmental trajectories and occupational pursuits . We discuss both sets of findings next.
Proficiency in visuospatial ability has long been associated with success in cognitively demanding educational tracks and occupations such as engineering, architecture, physics, chemistry, and surgery and is a salient characteristic of physical scientists . Yet, visuospatial ability is not routinely taught or assessed by schools and thus is not often developed and assessed in ways that influence students educational and career plans.
Racial And Ethnic Differences In Average Abilities
Sex differences in cognitive abilities and career achievement are complicated, but the fact that there are some tests and some areas of mathematics and science in which females, across all racial and ethnic groups, tend to excel, and some in which males, across all racial and ethnic groups, tend to excel, makes it difficult for any single theory such as motivation, learning, biology, or test-related anxiety to explain the difference. The consistency of the sex-related cognitive pattern of results is consistent with predictions based on an evolutionary perspective , but as we note later, there are many researchers who raise objections to evolutionary explanations for science and math data.
You May Like: What Does I Stand For In Physics
How To Sum Time In Excel
The Excel sum time formula is the usual SUM function, and applying the proper time format to the result is what does the trick.
Supposing you have a few project times in column B and you want to add them up. You write a simple SUM formula like =SUM and get the result in the default format, like hh:mm:ss.
In some cases the default time format works just fine, but sometimes you may want more, for example to display the total time as minutes and seconds, or seconds only. The good news is that no other calculations are required, all you have to do is apply custom time format to the cell with the SUM formula.
Right click the cell and select Format Cells in the context menu, or press Ctrl + 1 to open the Format Cells dialog box. Select Custom from the Category list and type one of the following time formats in the Type box:
- To display total time as minutes and seconds: :ss
- To display total time as seconds:
The result will look as follows:
Sex Discrimination And Occupational Success
Psychological scientists have studied sex discrimination in a number of ways. Social psychologists agree that the old-fashioned, overt sexism that existed several decades ago in the United States may have been replaced by unconscious, covert, modern sexism or neosexism in some situations . Studies investigating sex bias generally use one of two methodological approaches: experimental studies, in which a work product is submitted to raters for evaluation of its quality and half of the raters see it with a stereotypic male name as author and the other half see the same work product but with a stereotypic female name as author; and naturalistic studies examining experiences of sexism or evaluations or hiring of males and females in real work settings. The experimental studies have the advantage of experimental control but may lack external validity; the naturalistic studies supply the latter, and therefore these studies are perceived to be complementary.
You May Like: Algebra Road Trip Project Answer Key
How To Use This Difference Quotient Calculator
The procedure to use the difference quotient calculator is as follows:Step 1:;Enter two functions in the respective input fieldStep 2:;Now click the button Calculate Quotient to get the resultStep 3:;Finally, the difference quotient will be displayed in the new window
In calculus, the;difference quotient;is the formula used for finding the;derivative;which is the;difference quotient;between two points that are as close as possible which gives the rate of change of a function at a single point. The;difference quotient;was formulated by Isaac Newton.
Use Rounding To Estimate Differences
Here’s a quick review on rounding rules.
If the digit one place to the right of the target digit is less than 5, you round down.
If the digit one place to the right of the target digit is 5 or more, you round up.
When you round the minuend and subtrahend in a subtraction equation, you make the subtraction simpler.
You just have to remember to keep the difference close to the exact answer.
Also Check: Pre Algebra Order Of Operations Help
How To Find Sum Or Difference Of Math Problems
Math problems are diverse and can range in complexity from simple arithmetic to the upper levels of calculus. Understanding how to calculate the sum or difference of numbers is the foundation for many higher-level problems and an important skill in itself. When these numbers are added together , the resulting answer is called the “sum.” When a number is subtracted from another number , the result is known as the “difference.”
Sex Differences In Math And Science Abilities In The Tails Of The Distribution
Studying sex differences in mathematical and scientific abilities by examining differences at the population mean is useful but can lead to misleading conclusions if the distribution of test scores is not similar for males and females . This is particularly the case when the focus is on populations characterized by high abilities and the potential to become future mathematics or science professionals . Differences in population variance, as well as potential skew in these distributions, could lead to overrepresentation of one sex over the other at the extremes.
Don’t Miss: What Is The Molecular Geometry Of Ccl4
An Evolutionary Understanding Of Human Sex Differences
Evolutionary theory applies as well to human sex differences as it does to those of other species. However, the twin foundations of sexual selectionmale competition and female choiceare nuanced, in humans, by the existence of female competition and male choice; the two latter components follow from male investment in children. The combination is predicted to result in more subtle and perhaps smaller sex differences in humans than for many other species.
Human sex differences in physical size, upper-body musculature, rate and pattern of physical development, and other traits are consistent with the view that sexual selection has contributed to some currently observed sex differences . However, the relative importance of evolutionary and cultural influences on cognitive, behavioral, and social sex differences is the subject of vigorous debate .
Sex Hormones and Cognitive Sex Differences
In any case, data about the relation between prenatal exposure to androgens and sex differences in spatial abilities are mixed and difficult to interpret, especially in light of the complexity of assessing spatial abilities in very young children and in determining levels of prenatal hormone exposure . Moreover, there is a postnatal surge in androgens in males, but we do not know if or how it is related to the development of spatial cognition.
Trick To Remember The Difference
Math and maths are the standard forms of this word in American and British English, respectively.
Luckily, there is a very easy way to remember maths vs. math. Maths ends in the letter S, just like the river Thames in England. If you can link this bit of British geography to the British word maths, you should have no trouble remembering the usage cases for these variants.
Don’t Miss: Geometry Wars 2 Smile Achievement
How Do You Find The Percentage Difference In Chemistry
The percentage difference formula or the percent difference equation of two numbers a and b is \} \right| \times 100\%\end\). We use the percent difference formula in Chemistry to find the percentage difference between two experimental values. The percent difference formula in Physics is same as the above formula, where a and b are two experimental values.
Can The Common Difference In Ap Be Zero
Yes. The common difference in an arithmetic progression can be zero. As per the definition of an arithmetic progression , a sequence of terms is considered to be an arithmetic sequence if the difference between the consecutive terms is constant. Thus, an AP may have a common difference of 0.
And since 0 is a constant, it should be included as a common difference, but it kinda feels wrong for all the numbers to be equal while being in an arithmetic progression.
Read Also: Eoc Fsa Warm Ups Algebra 1 Answers
How To Find The Difference Between Two Numbers
I ran into a question on a practice test which said “What is the difference between -8 and -3? I am 13, and I am quite capable of subtracting negative numbers; I just did -8–3 to get my answer, making it -8+3, then making that -5. However, when I checked my answers, I was told that it was wrong, and the answer was 5.
When finding the difference between two numbers, do you subtract the bigger number from the smaller or vice versa?
Thank a lot!
- 8$\begingroup$”The difference between a and b” is ambiguous. It might mean $a-b$ or $b-a$. I suspect most people mean $|a-b|$, but I just try to avoid the phrase in practice.$\endgroup$;user137731Jan 3 ’16 at 22:46
- $\begingroup$Usually, the difference between $a$ anf $b$ denotes $\lvert a-b\rvert$.$\endgroup$Jan 3 ’16 at 22:47
- 4$\begingroup$It is ambiguous, but if forced to choose, I would say first minus second. You might contact who wrote the test and ask them. Usually professionally written tests are quite careful to not be ambiguous$\endgroup$Jan 3 ’16 at 22:49
- 4$\begingroup$Rejoice that you know the difference between $a-b$ and $b-a$, that’s a proper mathematical distinction . Take care in exams at your level that you understand what the examiner is asking . The game in exams is to get the marks. The game in maths is to get it correct. In exams, you play the examiner’s game .$\endgroup$
Additional Factors Influencing Sex Differences In Career Choices Of High
, when studying women in science, found that most of the observed sex differences in research productivity could be attributed to personal characteristics and the structural features of the employment setting. Having children was one factor associated with less engagement in mathematical and science careers for women but not for men. Sex differences in mathematical and science careers are indeed extremely complex and are surely influenced by the social structures in which individuals are situated, the neighborhood resources, and the networks of interaction in which they participate . The fact that social and environmental variables are important determinants of career success, however, does not mean that we cannot draw conclusions about the role of abilities, preferences, and other factors that may be responsible for producing sex disparities in participation, engagement, and achievement in the quantitative disciplines at the very highest levels. The SMPY studies clearly demonstrate that sex differences in mathematical and visuospatial abilities, the male tilt compared to female balance in ability profiles, and differing preferences and educational experiences all contribute to the sex differences in outcomes among the highly gifted.
Recommended Reading: What Is Mean Median Mode And Range In Math
Speculative Hypotheses On The Relation Of Neural Structures To Science And Mathematics
The state of knowledge on the neurobiology of sex differences does not permit strong statements, predictions, or recommendations. Especially lacking are large-scale studies in which science and mathematics abilities are rigorously measured and related to brain anatomy and physiology. Nonetheless, several tentative hypotheses can be proposed.
Anatomically, male brains appear to be optimized for connectivity within the hemispheres, while female brains appear to have better interhemispheric connectivity. For females, better interhemispheric communication confers an advantage in language and the ability to better integrate verbal-analytical with spatial-holistic modes of information processing. Biologically, females have higher cerebral blood flow, and the metabolic glucose rates show differences for women and men that vary with brain region. Activation studies support the notion that females perform better on tasks such as language processing that require bilateral activation, while males excel in tasks requiring focal activation of the visual association cortex. Studies by found that the right hemisphere may play a role in linguistic processing for mathematically precocious youth, a population that, as we discussed earlier, displays sex differences in mathematical and visuospatial abilities.
What Is The Difference Of Two Sets In Set Theory
- M.S., Mathematics, Purdue University
- B.A., Mathematics, Physics, and Chemistry, Anderson University
The difference of two sets, written A – B is the set of all elements of A that are not elements of B. The difference operation, along with union and intersection, is an important and fundamental set theory operation.
Read Also: What Is Figure Ground Perception Psychology
Other Identities Involving The Difference And Complements
There are many set identities that involve the use of the difference and complement operations. Some identities combine other set operations such as the intersection and union. A few of the more important are stated below. For all sets A, and B and D we have:
- A – A =
- DeMorgans Law I: C = AC BC
- DeMorgans Law II: C = AC BC
Date & Time Formula Wizard
Now that you know a bunch of different formulas to add and subtract times in Excel, let me show you the tool that can do it all. Okay, almost all 🙂
Here comes Ablebit’s Date & Time Formula Wizard for Excel:
In the Date & Time Wizard dialog window, you switch to the Add or Subtract tab, depending on which operation you want to perform, and do the following:
- Click the Show time fields link in the left part of the window.
- Supply values or cell references for the formula arguments. As you fill in the argument boxes, the wizard builds the formula in the selected cell.
- When finished, click the Insert Formula
That’s it! For example, this is how you can add the specified number of hours, minutes and seconds to the time in A4:
If you need to copy the formula to other cells, fix all references except the cell containing the original time with the $ sign like shown in the screenshot below . Then double-click the fill handle to copy the formula down the column and you are good to go!
If you are curious to try this tool in your own worksheets, you are welcome to download the 14-day trial version of our Ultimate Suite which includes this as well as 60 more time saving add-ins for Excel.
Read Also: Lesson 9.5 Geometry Answers