Answer :
Answer:
[tex]4 {x}^{3} - 400x = 4x(x + 10)(x - 10)[/tex]
Step-by-step explanation:
We want to factor
[tex]4 {x}^{3} - 400x[/tex]
First, we factor the GCF to get:
[tex]4x( {x}^{2} - 100)[/tex]
Now, we rewrite the expression in the parenthesis as difference of two squares.
[tex]4x( {x}^{2} - 100) = 4x( {x}^{2} - {10}^{2} )[/tex]
Recall that:
[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]
We apply this property to get:
[tex]4x( {x}^{2} - 100) = 4x(x + 10)(x - 10)[/tex]
Therefore the completely factored form of the given expresion is:
[tex]4x(x + 10)(x - 10)[/tex]