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

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Answer 1 · 2018-06-19T13:00:23

See a solution process below:

This is a special form of the quadratic function:

$color(red)(a)^2 - color(blue)(b)^2 = (color(red)(a) + color(blue)(b))(color(red)(a) - color(blue)(b))$

Let $color(red)(a)^2 = x^2$ then $sqrt(color(red)(a)^2) = sqrt(x^2) -> color(red)(a) = x$

Let $color(blue)(b)^2 = 64$ then $sqrt(color(blue)(b)^2) = sqrt(64) -> color(blue)(b) = 8$

Substituting gives:

$color(red)(x)^2 - color(blue)(64) = (color(red)(x) + color(blue)(8))(color(red)(x) - color(blue)(8))$

Answer 2 · 2018-06-19T13:56:53

$(x-8)(x+8)$

Given: $x^2-64$ .

Notice how $64=8^2$ .

$=x^2-8^2$

Use the difference of squares property, which states that $a^2-b^2=(a-b)(a+b)$ . Letting $x=a,b=8$ , we get:

$=(x-8)(x+8)$

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