Question

exponents and polynomials
factoring a perfect square trinomial with leading coefficient greater than 1
factor.
25w² + 60w + 36

Explanation:

Step1: Recall perfect square trinomial formula

A perfect square trinomial has the form \(a^2 + 2ab + b^2=(a + b)^2\) (or \(a^2-2ab + b^2=(a - b)^2\)). For the trinomial \(25w^2+60w + 36\), first identify \(a^2\) and \(b^2\).
We see that \(25w^2=(5w)^2\), so \(a = 5w\), and \(36 = 6^2\), so \(b = 6\).

Step2: Check the middle term

Now check if the middle term \(60w\) equals \(2ab\). Calculate \(2ab\): \(2\times(5w)\times6=60w\), which matches the middle term.

Step3: Factor using the formula

Since \(25w^2+60w + 36=(5w)^2+2\times(5w)\times6+6^2\), by the perfect square trinomial formula, it factors to \((5w + 6)^2\).

Answer:

\((5w + 6)^2\)