1Cademy - Factoring $$9y^2 + 24y + 16$$

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Perfect Square Trinomials Pattern

Example

Factoring $9y^2 + 24y + 16$

Factor the trinomial $9y^2 + 24y + 16$ by applying the perfect square trinomials pattern.

Step 1: Check if the trinomial fits the perfect square pattern $a^2 + 2ab + b^2$ .

Is the first term a perfect square? Yes: $9y^2 = (3y)^2$ , so $a = 3y$ .
Is the last term a perfect square? Yes: $16 = 4^2$ , so $b = 4$ .
Is the middle term $2ab$ ? Check: $2 \cdot 3y \cdot 4 = 24y$ . Yes, the middle term matches.

Step 2: Write the expression as the square of a binomial. Because the middle term is positive, use the pattern $(a + b)^2$ : $9y^2 + 24y + 16 = (3y + 4)^2$