How do you factor $2x^3 -128x$ ?

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Answer 1 · 2015-10-18T11:42:12

$2x(x-8)(x+8)$

Start by breaking down your initial expression in search of possible common factors

$2x^3 = color(blue)(2 * x) * x^2$

$128x = 64 * color(blue)(2 * x)$

This means that you can use $color(blue)(2x)$ as a common factor for these two terms

$2x^3 - 128x = 2x * (x^2 - 64)$

Notice that $64$ is a perfect square

$64 = 8 * 8 = 8^2$

which means that you are actually dealing with the difference of two squares

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

The bracket can thus be written as

$x^2 - 64 = x^2 - 8^2 = (x-8)(x+8)$

The expression will thus be equivalent to

$2x^3 - 128x = color(green)(2x(x-8)(x+8))$

How do you factor 2x^3 -128x2x^3 -128x?