Question

factor the trinomial below completely.

\\x^2 + 16xy + 64y^2\\

select the correct choice below and, if necessary, fill in the answer box to

a. \\x^2 + 16xy + 64y^2 = \quad\\ (factor completely.)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring special products

Step 1: Identify the pattern

The given expression is:

$$ x^2 + 16xy + 64y^2 $$

This fits the perfect square trinomial pattern:

$$ a^2 + 2ab + b^2 = (a + b)^2 $$

Step 2: Determine \( a \) and \( b \)

Compare the terms:

$$ a^2 = x^2 \implies a = x $$

$$ b^2 = 64y^2 \implies b = 8y $$

Check the middle term:

$$ 2ab = 2(x)(8y) = 16xy $$

Since the middle term matches, we can write the factored form.

Step 3: Factor the expression

$$ (x + 8y)^2 $$

Answer:

A. \( x^2 + 16xy + 64y^2 = (x + 8y)^2 \)