Question

Consider these shapes.

3x² + 2
Shape A
7x² + 4x + 8
Shape B
3x²+2
If shape B is a square, which polynomial represents the differencer

Answer 1

Choice A:
`2x^4+12x^3+26x^2+8x+12`

Explanation:

This can be done without computing the entire product and difference with a little bit of thought. If you look at the answer choices they have different values for the coefficient of
`x^4` Choices B and C do not even have a term for
`x^4`

So if we focus on only the part of the multiplication which will produce an
`x^4` term we can find the right choice

The area of Shape A is (3x² + 2)(7x² + 4x + 8)

One of the terms arises from 3x² x 7x² =
`21x^4`

The area of Shape B = (3x²+2)(3x^2+2)

So the

Look at the answer choices.
The first component has x term
`x^4` which is obtained by multiplying

(3x²)(3x²) =
`9x^4`

If we subtract the area of Shape B from Shape A , we get the
`x^4` term as

`21x^4 - 9x^4 = 12x^4`

The only choice which has
`12x^4` as a term is the first one, Choice A

So answer is Choice A:
`2x^4+12x^3+26x^2+8x+12`

Answer 2

12x^(4)+12x^(3)+26x^(2)+8x+12

Explanation:

Plato/Edmentum