Question

Kylie explained that (–4x + 9)2 will result in a difference of squares because (–4x + 9)2 = (–4x)2 + (9)2 = 16x2 + 81. Which statement best describes Kylie’s explanation?

Kylie is correct.
Kylie correctly understood that it is a difference of squares, but she did not determine the product correctly.
Kylie did not understand that this is a perfect square trinomial, and she did not determine the product correctly.
Kylie determined the product correctly, but she did not understand that this is a perfect square trinomial.

Answer 1

The expression (-4x + 9)^2 cannot be equal to (-4x)^2 + 9^2 because it is actually equal to the product of two factors (3 + 2sqrt x) (3- 2 sqrt x). One cannot use obviously distributive property. Hence the answer to this problem should be C. as she did not understand both perfect square trinomial and did not determine the product 

Answer 2

The correct answer is: (C) Kylie did not understand that this is a perfect square trinomial, and she did not determine the product correctly.

Explanation:
Kylie did not determine the product correctly, as the perfect-square trinomials are of the form:
$a^2x^2 \pm 2axb \pm b^2$

and are expressed in the squared-binomial form as:
$(ax \pm b)^2$

The correct product would be:
$(-4x + 9)^2 = (-4x)^2 + 2(-4)(9)x + (9)^2 = 16x^2 - 72x + 81$

Hence the correct answer is that Kylie did not understand that this is a perfect square trinomial, and she did not determine the product correctly (Option C).