Question

Tim wrote the expressions g^2-2gh-h^2 and -g(g+2h-1) -h^2. He substituted 0 for g and 1 for h, and said the expressions are equivalent. Is he correct? Explain.

Answer 1

Yes. The result both gives -1.

Explanation:

The expressions are
`g^2-2gh-h^2` and
`-g(g+2h-1) -h^2`

If he substituted g=0 and h=1

`g^2-2gh-h^2=0^2-(2X0X1)-1^2=0-0-1=-1`

`-g(g+2h-1) -h^2=-0(0+(2X1)-1)-1^2=0-1=-1`

`-1^2=-1 and 0X a=0`

The result both gives -1.