Ex.12.3 Q5 Algebraic Expressions Solution - NCERT Maths Class 7

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Question

When \(a = 0\), \(b = \,– 1\), find the value of the given expressions:

(i) \(2a+\text{ }2b\)

(ii) \(2{{a}^{2}}+{{b}^{2}}+\text{ }1\)

(iii) \(2{{a}^{2}}b+\text{ }2a{{b}^{2}}+ab\)

(iv) \({{a}^{2}}+ab+\text{ }2\)

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 \(0\) and \(b\) is \(–1\)

(i) \(2a+\text{ }2b\)

\[\begin{align}& = \left( {2 \times 0} \right) + \left( {2 \times - 1} \right)\\& = 0 + \left( { - 2} \right)\\{\rm{ Ans }} & = - 2\end{align}\]

(ii) \(2{{a}^{2}}+{{b}^{2}}+\text{ }1\)

\[\begin{align}& = \left( {2 \times {0^2}} \right) + {\left( { - 1} \right)^2} + 1\\ & = 0 + 1 + 1\\& = 2\end{align}\]

(iii) \(2{{a}^{2}}b+\text{ }2a{{b}^{2}}+ab\)

\[\begin{align}& = 2 \times 0 \times 0 \times - 1 + \left( {2 \times 0 \times - {1^2}} \right) + 0 \times - 1\\& = 0 + 0 + 0\\{\rm{ Ans }} & = 0\end{align}\]

(iv) \({{a}^{2}}+ab+\text{ }2\)

\[\begin{align}& = {0^2} + 0 \times - 1 + 2\\& = 0 + 0 + 2\\{\rm{ Ans }} & = 2\end{align}\]