How do you factor the expression $25 x^{2} - 64$ $25x^2-64$ ?

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How do you factor the expression $25 x^{2} - 64$ $25x^2-64$ ?

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Answer 1 · 2017-12-08T20:12:32

$25 x^{2} - 64 = (5 x - 8) (5 x + 8)$ $25x^2-64 = (5x-8)(5x+8)$

Explanation:

The difference of squares identity can be written:

$A^{2} - B^{2} = (A - B) (A + B)$ $A^2-B^2=(A-B)(A+B)$

In the given example, both $25 x^{2} = {(5 x)}^{2}$ $25x^2 = (5x)^2$ and $64 = 8^{2}$ $64 = 8^2$ are perfect squares. So we can put $A = 5 x$ $A=5x$ and $B = 8$ $B=8$ to find:

$25 x^{2} - 64 = {(5 x)}^{2} - 8^{2} = (5 x - 8) (5 x + 8)$ $25x^2-64 = (5x)^2-8^2 = (5x-8)(5x+8)$

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How do you factor the expression $25 x^{2} - 64$ $25x^2-64$ ?

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How do you factor the expression $25 x^{2} - 64$ $25x^2-64$ ?