Question

Evaluate g(p)•h(p) by modeling or by using the distribution property

g(p) = (p-2) and h(p) = (p3

Answer 1

`g(p) \cdot h(p) = p^(4)+2 p^(3)-8 p^(2)-2p+4`

Solution:

Given data:

`g(p)=(p-2)` and
`h(p)=\left(p^(3)+4 p^(2)-2\right)`

To find
`g(p) \cdot h(p)`:

`g(p) \cdot h(p)= (p-2)\cdot \left(p^(3)+4 p^(2)-2\right)`

Distributive property:
`a(b+c)=ab + ac`

`= p\left(p^(3)+4 p^(2)-2\right) -2\left(p^(3)+4 p^(2)-2\right)`

`= \left(p^(4)+4 p^(3)-2p\right) +\left(-2p^(3)-8 p^(2)+4\right)`

`= p^(4)+4 p^(3)-2p-2p^(3)-8 p^(2)+4`

Arrange and add/subtract same powers.

`= p^(4)+(4 p^(3)-2p^(3))-8 p^(2)-2p+4`

`= p^(4)+2 p^(3)-8 p^(2)-2p+4`

Hence
`g(p) \cdot h(p) = p^(4)+2 p^(3)-8 p^(2)-2p+4`