Question

How do you factor ${{\left( x+a \right)}^{2}}-{{b}^{2}}=0$ ?

Answer 1

Hint: In this question, we have to find the factors of an algebraic expression. So, we will use the algebraic identity and the basic mathematical rules to get the required solution. We will first compare the given algebraic expression with the algebraic identity ${{m}^{2}}-{{n}^{2}}=0$ . Then, we will find the value of m and n. In the last, we will put the value of m and n in equation $\left( m+n \right)\left( m-n \right)=0$ , to get the required result for the solution.

Complete step by step solution:
According to the question, we have to find the factors of an algebraic expression.
So, we will apply the algebraic identity and the basic mathematical rules to get the required result.
The expression given to us is ${{\left( x+a \right)}^{2}}-{{b}^{2}}=0$ ---------------- (1)
Now, we will apply the algebraic identity, that is we know
If ${{m}^{2}}-{{n}^{2}}=0$ , then --------- (2)
$\left( m+n \right)\left( m-n \right)=0$ -------- (3)
Now, on comparing equation (1) and (2), we get the value of m and n equal to $x+a$ and $b$ respectively.
Thus, on putting the value m and n in equation (3), we get
 $\left( x+a+b \right)\left( x+a-b \right)=0$ which is the required solution.
Therefore, for the algebraic expression ${{\left( x+a \right)}^{2}}-{{b}^{2}}=0$ , their factors are equal to $\left( x+a+b \right)\left( x+a-b \right)$ .

Note: While solving this equation, do step-by-step calculations properly to avoid confusion and mathematical errors. One of the methods to check your answer is use the distributive property in the solution, that is open the brackets of the solution and make the mathematical calculations, which is equal to the algebraic expression given in the problem.