QuestionFactor. $9 y^{2}+48 y+64$

Studdy Solution

STEP 1

1. The expression is a quadratic trinomial.
2. The expression can be factored into the form $(ay + b)^2$ if it is a perfect square trinomial.
3. If the expression is not a perfect square trinomial, it can be factored using other methods such as grouping or the quadratic formula.

STEP 2

1. Check if the trinomial is a perfect square.
2. Factor the trinomial if it is a perfect square.

STEP 3

Check if the trinomial $9y^2 + 48y + 64$ is a perfect square trinomial. A perfect square trinomial takes the form $(ay + b)^2 = a^2y^2 + 2aby + b^2$ .
- Identify $a^2 = 9y^2$ , so $a = 3y$ . - Identify $b^2 = 64$ , so $b = 8$ . - Check if $2ab = 48y$ .
Calculate $2ab$ :
$2 \cdot 3y \cdot 8 = 48y$
Since $2ab = 48y$ , the trinomial is a perfect square.

STEP 4

Since the trinomial is a perfect square, factor it as $(ay + b)^2$ .
$(3y + 8)^2$
Thus, the factorization of the trinomial $9y^2 + 48y + 64$ is:
$\boxed{(3y + 8)^2}$

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