Question

The Special Factoring Formula for a “perfect square” is $A^2+2AB+B^2=\_\_\_\_\_$. So,$x^2+10x+25=\_\_\_\_\_$

Short answer

The Special Product Formula for the “perfect square” is $A^2+2AB+B^2={\left(A+B\right)}^2$. So,$x^2+10x+25={\left(x+5\right)}^2$

Step-by-step solution

Step 1. Apply the Factoring 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$x^2+10x+25$

Here

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

Step 3. Solve the expression.

Substitute the values in the perfect square formula to get:

$\begin{array}{l}{x}^2+10x+25=x^2+2\cdot x\cdot 5+5^2\\ \Rightarrow x^2+10x+25={\left(x+5\right)}^2\end{array}$