Question

In the following exercises, factor each trinomial of the form $x^2+bxy+c^2$

$r^2+15rs+36s^2$

Short answer

The factorization of$r^2+15rs+36s^2$is$(r+12s)(r+3s)$

Step-by-step solution

Step 1. Given information

Given expression is$r^2+15rs+36s^2$

Step 2. Find the last terms of the trinomials.

The factor of the expression:

The factor of 36	Sum of factor
2, 18	2 + 18 = 20
4, 9	4 + 9 = 13
12, 3	12 + 3 = 15

Step 3. Factorization

Use $12$and $3$as the last terms of the trinomials.

$r^2+15rs+36s^2=(r+12s)(r+3s)$

Step 4. Check

$$\begin{gathered} (r+12s)(r+3s)=r^2+12rs+3rs+36s^2 \\ =r^2+15rs+36s^2 \end{gathered}$$