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Difference of Squares

One of the most important formulas on the test is the difference of squares:
 
 

 

Caution: a sum of squares,
x2 + y2, does not factor.

 

Example

If x ≠ –2, then
A.  2(x – 2)
B.  2(x – 4)
C.  8(x + 2)
D.  x – 2
E.  x + 4

 

In most algebraic expressions involving multiplication or division, you won’t actually multiply or divide, rather you will factor and cancel, as in this problem.

 

 

 by the distributive property ax + ay = a(x + y)

 

 by the difference of squares x2 – y2 = (x + y)(x – y)

 

2(x – 2) by canceling common factors

 

The answer is (A).
 





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