1Cademy - Factoring $$16z^2

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Perfect Square Trinomials Pattern

Example

Factoring $16z^2 - 72z + 81$

Factor the trinomial $16z^2 - 72z + 81$ 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: $16z^2 = (4z)^2$ , so $a = 4z$ .
Is the last term a perfect square? Yes: $81 = 9^2$ , so $b = 9$ .
Is the middle term $-2ab$ ? Check: $-2(4z)(9) = -72z$ . 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 $(a - b)^2$ : $16z^2 - 72z + 81 = (4z - 9)^2$