Question

Is
`a^2(a-0.4)^3` completely factored?

The original question was to completely factor this:

`a^5-0.064a^2`

Answer 1

`\bf a^2* (a - 0.4)(a^2 + 0.4a + 0.16)`

Explanation:

Factorize:

First take out the common term a².

`a^5 - 0.064a^2= a^2*(a^3 - 0.064)\\\\`

Now, factorize using the identity a³ - b³

a³ - b³ = (a - b) (a² + ab + b²)

`a^2 * (a^2 - 0.064) = a^2 * (a^3 - 0.4^3)`

`= a^2 * (a - 0.4) * (a^2 + a*0.4 + 0.4^2)\\\\=a^2 * (a - 0.4)(a^2 + 0.4a + 0.16)`