Question

(5x^5) - (80x^3)
factoring

Answer 1

Factoring the term
`(5x^5) - (80x^3)` we get
`\mathbf{5x^3(x-4)(x+4)}`

Explanation:

We need to factor the term
`(5x^5) - (80x^3)`

First we can see that
`5x^3` is common in both terms

So, taking
`5x^3` common:

`(5x^5) - (80x^3)\\=5x^3(x^2-16)`

We can write
`x^2-16` as
`(x)^2-(4)^2`

`=5x^3((x)^2-(4)^2)`

Now we can solve
`(x)^2-(4)^2` using the formula:
`a^2-b^2=(a+b)(a-b)`

We can write:

`=5x^3((x)^2-(4)^2)\\=5x^3(x-4)(x+4)`

So, factoring the term
`(5x^5) - (80x^3)` we get
`\mathbf{5x^3(x-4)(x+4)}`