Question

Can someone help me please

Answer 1

`g(x)=-x^2-8x-22`

Explanation:

Perform the multiplication and addition:

`g(x)=-(x+4)^2-6=-(x^2+8x+16)-6=-x^2-8x-16-6\\\\g(x)=-x^2-8x-22`

_____

Comment on the squaring

There are several ways you can find the square (x+4)².

1. Use your knowledge that (x+a)² = x²+2ax+a².
2. Use FOIL* to compute (x+4)(x+4) = x² +4x +4x +4² = x²+8x+16
3. Use the distributive property: (x+4)(x+4) = x(x+4) +4(x+4) = x² +4x +4x +4² (same as FOIL for two binomials)

__

* FOIL is mnemonic for {First, Outer, Inner, Last} referring to pairs of terms in the factors (x +a)(x +b). The x terms are the First terms. The Outer terms are the first x and b. The Inner terms are "a" and the second x. The Last terms are "a" and "b". You are to form the sum of those pairs of terms to find the product of the binomials.