Question

How do you multiply `(w-6)(2w+8)`?

Answer 1

`(w-6)(2w+8) =2w^2-4w-48`

Explanation:

To multiply sums in parenthesis, one needs to distribute each term from one factor over the terms of the other and add the resulting terms together. For example:

`(a + b)(x+y) = a(x+y) + b(x+y) = ax+ay+bx+by`

We need to be careful when some of the terms in the factors are negative, as in our example, but the same rules apply

`(w-6)(2w+8) = w(2w+8)-6(2w+8)`
`implies 2w^2+8w-12w-48`

Now we need to gather like terms which simplifies our expression to

`implies 2w^2-4w-48`