The result is a difference of two squares because the expression is a subtraction or difference between two terms
Difference Between Two Squares. Video 120 on www.corbettmaths.com. Question 1: Factorise each of the following. (a) x² ? 25. (b) y² ? 49. (c) w² ? 100.
We can also use the expansion of the difference of two squares to rationalise more complicated expressions involving surds. Example.
Difference of two squares. Expanding and exactly two factors – itself and one 2 3
Oct 11 2013 3:07B Difference of two squares ... Apply the distributive law to the expansion of algebraic expressions
question go to Pearson Places and download the Recall Worksheet from (b) 1 Expand both sets of brackets by ... The Difference of Two Squares rule:.
If and are perfect squares then ? is called the difference of two squares. Notice that ( + )( ? ) = ? + ? = ?. Thus. EXAMPLE 7. Expand and simplify:.
Expanding binomial products. Perfect squares and difference of perfect squares. Factorising algebraic expressions. Factorising the difference of two squares.
The answers all turn out to be the difference of two squares. Here is a rule to help you memorize the result: RULE: When multiplying two binomials that
When you expand one set of brackets you must multiply everything inside the An expression in the form x2 – y2 is called the difference of two squares.
Worksheet by Kuta Software LLC Algebra 1 Difference of Two Squares Name_____ ID: 1 Date_____ Period____ ©b i2X0s1l6u HKzumttaR [SRoSfQtUwcajrWeM nLgLMCS h a XAPl_lf ]rLiRglh[tXsK erJevsenrzvxend[ -1-Factor each completely 1) 49b2 - 25 2) 81r2 - 25 3) 121n2 - 25 4) 9n2 - 1 5) 169n2 - 81 6) 81k2 - 169
Difference Between Two Squares Video 120 on www corbettmaths com Question 1: Factorise each of the following (a) x² ? 25 (b) y² ? 49 (c) w² ? 100 (d) x² ? 4
Expanding and factorising are often used in algebra We ‘distribute’ multiplication through addition or subtraction Often referred to as either expanding the brackets or removing the brackets For example: Expand – 2– 22 ++ 2×=2+6 http://passyworldofmathematics com/expanding-brackets-using-distributive-rule/ Factorise
This result is known as the difference of two squares The product is equal to the difference of the two squares Task C ????=(5+3)(5?3) ????=52?32 Construct shapes of your own to show this idea: Can you explain why the rectangle must always have the same area as the difference of squares?
Corbettmaths - Difference between two squares Extension Task 1: Explain what the picture above represents Extension Task 2: lot of numbers can be written as the difference between two squares For example 15 = 8² - 7² 20 = 6² - 4² Can you write all the numbers from 1 to 30 as the difference of two squares? Investigate the odd numbers
Expand the following using the perfect squares: (2a + 5)2 (b) (5a – 3)2 (c) (m + 3)2 Q4 Expand using knowledge of difference of two squares: (x + y) (y – x) (b) (3m – n) (3m + n) (c) (d) (2y – 3x) (2y + 3x) (d) (d – 7)2 (y + 6) (y – 6) Q5 Factorise the following: 2a2b – 4ab (b) (d) 36a2b + 48a2 mn2 – m2n (c) -15 - 20m Q6