What is the completely factored form of x2 – 16xy + 64y2? a. xy(x – 16 + 64y) b. xy(x + 16 + 64y) c. (x – 8y)(x – 8y) d. (x + 8y)(x + 8y)

your answer will be c. (x-8y) (x-8y)

answer: option c. (x – 8y)(x – 8y)

explanation:

1) note that the expression has 3 terms, so it is a trinomial.

2) note that the first and third terms are perfect squares:

3) note that the second term is equal to double of the product of the square roots of the first and second terms:

4) in consequence, the trinomial is a perfect square trinonial, which means that its factored form is a square binomial:

5) finally, note that (x - 8y)² = (x - 8y) (x - 8y) which is the choice c.

i think the answer is b