Question

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

Answer 1

See a solution process below:

Explanation:

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

`(x-8)(x+8)`

Explanation:

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)`