Question

The Special Factoring Formula for the “difference of squares” is$A^2-B^2=\_\_\_\_\_$. So,$4x^2-25=\_\_\_\_\_$

Short answer

The Special Product Formula for the “difference of squares” is $A^2-B^2=\left(A+B\right)\left(A-B\right)$. So,$4x^2-25=\left(2x-5\right)\left(2x+5\right)$

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 $4x^2-25$

Here

$\begin{array}{l}{A}^2=4x^2,B^2=25\\ \Rightarrow A=2x,B=5\end{array}$

Step 3. Solve the expression.

Substitute the values in the Factoring formula to get:

$\begin{array}{l}4x^2-25={\left(2x\right)}^2-5^2\\ \Rightarrow 4x^2-25=\left(2x-5\right)\left(2x+5\right)\end{array}$