Question

${\text{a}}^2{\text{-b}}^2$ is equal to

• A. $({\text{a-b)}}^2$
• B. $(\text{a-b)(a-b)}$
• C. $(\text{a+b)(a-b)}$
• D. $(\text{a+b)(a+b)}$

Answer 1

The correct option is C

$(\text{a+b)(a-b)}$

Solving the identity:

We know the identity ${\text{a}}^2{\text{-b}}^2\text{=(a+b)(a-b)}$

If we solve the R.H.S of the equation we get

$$\begin{gathered} ({\text{a+b)(a-b)=a}}^2{\text{-ab+ba-b}}^2 \\ {\text{=a}}^2{\text{-ab+ab-b}}^2\text{(here ab=ba)} \\ ={\text{a}}^2{\text{-b}}^2 \end{gathered}$$

Hence option(C) is the correct answer