Ex.12.3 Q5 Algebraic Expressions Solution - NCERT Maths Class 7
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) \(2{{a}^{2}}b+\text{ }2a{{b}^{2}}+ab\)
\[\begin{align} &= \left[ \begin{array}{l}\,\,2 \times 0 \times 0 \times - 1 + \\\left( {2 \times 0 \times - {1^2}} \right) + 0 \times - 1\end{array} \right]\\ &= 0 + 0 + 0\\{\rm{Ans}} &= 0\end{align}\]
(iv) \({{a}^{2}}+ab+\text{ }2\)
\[\begin{align}& = {0^2} + 0 \times - 1 + 2\\& = 0 + 0 + 2\\{\rm{ Ans }} & = 2\end{align}\]