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) \({a^2} - {b^2}\)

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) \({a^2} - {b^2}\)

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