Question

Factor the expression completely.

$r^2-6rs+9s^2$

Short answer

The solution$r^2-6rs+9s^2={\left(r-3s\right)}^2$

Step-by-step solution

Step 1. Apply the “square of the difference” formula.

If A and B are any real numbers or algebraic expressions, then

$A^2-2AB+B^2={\left(A-B\right)}^2$

Step 2. Analyze the given expression.

Given$r^2-6rs+9s^2$

Here

$\begin{array}{l}{A}^2=r^2,B={\left(3s\right)}^2\\ \Rightarrow A=r,B=3s\end{array}$

Step 3. Solve the expression.

Substitute the values in the square of the difference formula to get:

$\begin{array}{l}{r}^2-6rs+9s^2=r^2-2\cdot r\cdot 3s+{\left(3s\right)}^2\\ \Rightarrow r^2-6rs+9s^2={\left(r-3s\right)}^2\end{array}$