Question

The factored form of 4a3b5 − 16a5b2 + 12a2b3 is ?

Answer 1

4a^2b^2(ab^3-4a^3+3b)

Answer 2

The factored form of
`4a^3b^5-16a^5b^2+12a^2b^3` is
`4a^2b^2\left(ab^3-4a^3+3b\right)`.

Explanation:

To find the factored form of
`4a^3b^5-16a^5b^2+12a^2b^3` you must:

Apply exponent rule:
`a^(b+c)=a^ba^c`

`a^2b^3=a^2b^2b,\:a^5b^2=a^2a^3b^2,\:a^3b^5=a^2ab^2b^3`

So, we can write our expression as
`4a^2ab^2b^3-16a^2a^3b^2+12a^2b^2b`.

Next, rewrite 12 as
`3\cdot \:4` and -16 as
`4\cdot \:4`

`4a^2ab^2b^3+4\cdot \:4a^2a^3b^2+3\cdot \:4a^2b^2b`

Factor out common term:
`4a^2b^2`

Therefore,

`4a^3b^5-16a^5b^2+12a^2b^3= 4a^2b^2\left(ab^3-4a^3+3b\right)`