Question

How do I factor the polynomial 4x to the third minus 400x

Answer 1

Answer:

$4 {x}^{3} - 400x = 4x(x + 10)(x - 10)$

Step-by-step explanation:

We want to factor

$4 {x}^{3} - 400x$

First, we factor the GCF to get:

$4x( {x}^{2} - 100)$

Now, we rewrite the expression in the parenthesis as difference of two squares.

$4x( {x}^{2} - 100) = 4x( {x}^{2} - {10}^{2} )$

Recall that:

${a}^{2} - {b}^{2} = (a + b)(a - b)$

We apply this property to get:

$4x( {x}^{2} - 100) = 4x(x + 10)(x - 10)$

Therefore the completely factored form of the given expresion is:

$4x(x + 10)(x - 10)$