Question

The Special Product Formula for the “product of the sum and difference of terms” is $\left(A+B\right)\left(A-B\right)=\_\_\_\_\_$. So,$\left(5+x\right)\left(5-x\right)=\_\_\_\_\_$

Short answer

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

Step-by-step solution

Step 1. Apply the special product formula of “product of the sum and difference of terms”.

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

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

Step 2. Analyze the given expression.

Given$\left(5+x\right)\left(5-x\right)$

Herewidth="82">A=5,B=x

Step 3. Solve the expression.

Substitute the values in the product of the sum and difference of terms formula to get:

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