# Ex.12.3 Q4 Algebraic Expressions Solution - NCERT Maths Class 7

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## Question

If $$a = 2$$, $$b =\, – 2$$, find the value of:

(i) $${a^2} + {b^2}$$

(ii) $${a^2} + ab + {b^2}$$

(iii) $${a^2} - {b^2}$$

Video Solution
Algebraic Expressions
Ex 12.3 | Question 4

## Text Solution

What is Known?

Value of $$a$$ and $$b$$

What is unknown?

Value of the given expressions.

Reasoning:

This is based on concept of putting given value of variable and then performing the arithmetic operation as given in the question.

Steps:

Value of $$a$$ is given as $$2$$ and $$b$$ is $$-2$$

(i) $${a^2} + {b^2}$$

\begin{align}& = {2^2} + {\left( { - 2} \right)^2}\\& = \left( {2 \times 2} \right) + \left( { - 2 \times - 2} \right)\\& = 4 + 4\\{\rm{Ans}} & = 8\,\end{align}

(ii) $${a^2} + ab + {b^2}$$

\begin{align} & = {2^2} + \left\{ {\left( 2 \right) \times \left( { - 2} \right)} \right\} + {\left( { - 2} \right)^2}\\& = 4 + \left( { - 4} \right) + 4\\& = 4 - 4 + 4\\{\rm{Ans}} & = 4\,\end{align}

(iii) $${a^2} - {b^2}$$

\begin{align}& = {2^2} - {\left( { - 2} \right)^2}\\& = 4 - 4\\{\rm{ Ans}} & = 0\end{align}

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