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use the FOIL method to multiply the two binomials.

(a+b)(a+(−b))=a⋅a+a⋅(−b)+b⋅a+b⋅(−b)                                     =a2−ab+ab−b2(a+b)(a+(−b))=a⋅a+a⋅(−b)+b⋅a+b⋅(−b)                                     =a2−ab+ab−b2

Notice that the middle terms are opposite and add to a zero pair.

So, (a+b)(a+(−b))=a2b2(a+b)(a+(−b))=a2b2.

In other words, the product of a+ba+b and a−ba−b is the square of aa minus the square of bb.


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If you are referring to the sum and difference of binomial, their product is called difference of two squares.

This is the pattern:

(a + b)     (a - b)          =  a² - b²
(sum)  (difference)    (difference of two squares)

Knowing this pattern, you don't have to use the longer process of finding the product either through F-O-I-L or other method.


(5x + 4) (5x - 4) = 25x² - 16

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