Question

Factor the expression completely.

$4t^2-9s^2$

Short answer

The solution$4t^2-9s^2=\left(2t-3s\right)\left(2t+3s\right)$

Step-by-step solution

Step 1. Apply the Factoring Formula.

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

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

Step 2. Analyze the given expression.

Given$4t^2-9s^2$

Here

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

Step 3. Solve the expression.

Substitute the values in the Factoring formula to get:

$\begin{array}{l}4t^2-9s^2={\left(2t\right)}^2-{\left(3s\right)}^2\\ \Rightarrow 4t^2-9s^2=\left(2t-3s\right)\left(2t+3s\right)\end{array}$