Question

How do you multiply `-p^2 (p-11)`?

Answer 1

Use the distributive property (also known as the distributive law or rule).

Explanation:

The distributive property says that for any numbers `a, b, "and " c`, we have:

`a(b+c) = a*b+b*c`

It may help to also point out that:

`p` may be thought of as `1p` and
`-p^2` is `-1p^2`.

Finally, `p-11` is the same as `p + (-11)`

So when we distribute, we get:

`-p^2(p-11) = -p^2(p+(-11))`

`= -p^2*p +(-p^2)(-11)`

`= -p^3 +(11p^2)`

`= -p^3+11p`

With experience, it becomes quicker to see that "when we distribute a minus sign, we have to change the signs" so, for example:
`-2(4x-7) = -8x+14`
and
`-3(-5x-9) = 15x+27`
and
`-x(-x+4) = x^2-4x`