1Cademy - Factoring $$64y^2

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Perfect Square Trinomials Pattern

Example

Factoring $64y^2 - 80y + 25$

Factor the trinomial $64y^2 - 80y + 25$ 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: $64y^2 = (8y)^2$ , so $a = 8y$ .
Is the last term a perfect square? Yes: $25 = 5^2$ , so $b = 5$ .
Is the middle term $-2ab$ ? Check: $-2(8y)(5) = -80y$ . Yes, the middle term matches.

Step 2: Write the expression as the square of a binomial. Because the middle term is negative, use the pattern $(a - b)^2$ : $64y^2 - 80y + 25 = (8y - 5)^2$