Question

What is the product (-6a^3b+2ab^2)(5a^2-2ab^2-b)

Answer 1

-30a^5*b+12a^4b^2+6a^3b^2+10a^3b^2-4a^2b^3-2ab^3

Answer 2

`-30a^5b+12a^4b^3+16a^3b^2-4a^2b^4-2ab^3` is the product of
`(-6a^3b+2ab^2)(5a^2-2ab^2-b)`

Explanation:

Using the exponent rule:

`x^a \cdot x^b = x^(a+b)`

To find the product of:

`(-6a^3b+2ab^2)(5a^2-2ab^2-b)`

`-6a^3b(5a^2-2ab^2-b)+2ab^2(5a^2-2ab^2-b)`

Using distributive property and exponent rules:
`a \cdot (b+c) = a\cdot b+ a\cdot c`

⇒
`-30a^5b+12a^4b^3+6a^3b^2+10a^3b^2-4a^2b^4-2ab^3`

Combine like terms;

`-30a^5b+12a^4b^3+16a^3b^2-4a^2b^4-2ab^3`