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

Dec 8, 2017

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

Explanation:

The difference of squares identity can be written:

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

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

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