Question

How do you multiply `(4x - 7) ( - 5x ^ { 2} - 7x + 8)`?

Answer 1

See the explanation below of the steps. The solution is:

`-20x^3+7x^2+81x-56`

Explanation:

The key is to ensure that each element in one bracket is multiplied by each element in the other. Since there are 3 in one and 2 in the other, there should be 6 terms, after the multiplication and before we collect like terms.

I'm going to do it by first multiplying the first term in the first bracket by each term in the second, then multiplying the second term in the first bracket by each term in the second:

`(4x−7)(−5x^2−7x+8)`
`=-20x^3-28x^2+32x+35x^2+49x-56`

Then we can collect 'like terms' among these 6 terms to simplify:

`-20x^3+7x^2+81x-56`