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Algebra Homework Help : Factorization - Difference of Two Squares

 
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How to factor a difference of two squares ?

The difference of two squares is commonly encountered in algebra and can be factored as follows :

 

a2 − b2 = (a + b)(a − b)

 

This is easily verified by expansion as shown below.
(a + b)(a − b) = a(a − b) + b(a − b) = a2 − ab + ba − b2 = a2 − b2

 

Thus, the difference of two squares is a binomial expression where the two terms are perfect squares with one term positive and the other negative.

 

Example : 32x2 − 18 = 2(16x2 − 9) = 2(4x + 3)(4x − 3)
In the above example, first 2 is factored out. Then what's left is the difference of two squares, which can be factored further. The square root of the first term (16x2) is 4x while the square root of the second term (9) is 3.


 Practice Exercise for Algebra Module on Difference of Two Squares

 

 
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