Question

How do you multiply `(2m^2 + n)(3n^2 + 6mn - m^2)`?

Answer 1

`(2m^2 + n)(3n^2 + 6mn -m^2) = – 2 m^4 + 12 m^3n + 6m^2n^2 – m^2n + 6mn^2 + 3n^3`

Explanation:

We use the distributive property of multiplication.

`(2m^2 + n)(3n^2 + 6mn - m^2) = 2m^2(3n^2 + 6mn - m^2) + n(3n^2 + 6mn - m^2)`

`= (6m^2n^2 + 12 m^3n – 2 m^4) + (3n^3 + 6mn^2 – m^2n)`

Now we remove parentheses and arrange the terms in descending powers of `m` and ascending powers of `n`.

`(2m^2 + n)(3n^2 + 6mn -m^2) = – 2 m^4 + 12 m^3n + 6m^2n^2 –m^2n + 6mn^2 + 3n^3`