Ex.12.3 Q2 Algebraic Expressions Solution - NCERT Maths Class 7

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Question

 If \(p = \,– 2\), find the value of:

(i) \(4p + 7\)

(ii) \(- 3{p^2} + 4p + 7\)

(iii) \(- 2{p^3} - 3{p^2} + 4p + 7\)

Text Solution

What is known?

Value of \(p\).

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 \(p\) is given as \(- 2\)

(i) \(4p + 7\)

\[\begin{align}& = 4 \times - 2 + \left( 7 \right)\\& = - 8 + 7\\{\rm{ Ans }} & = - 1\end{align}\]

(ii) \(- 3{p^2} + 4p + 7\)

\[\begin{align}&= - 3 \times {{\left( { - 2} \right)}^2} + \,4 \times \left( { - 2} \right) + 7\\& = \left( { - 3 \times - 2 \times - 2} \right) + \left( { - 8} \right) + 7\\& = - 12 - 8 + 7\\{\rm{ Ans }} & = - 13\end{align}\]

(iii) \(- 2{p^3} - 3{p^2} + 4p + 7\)

\[\begin{align}& =-2{{\left( -2 \right)}^{3}}-3{{\left( -2 \right)}^{2}}+4\left( -2 \right)+7 \\ & =-2\times -2\times -2\times -2\left( 3\times -2\times -2 \right)+\left( 4\times -2 \right)+7 \\ & =16\left( 12 \right)+\left( -8 \right)+7 \\ \text{Ans} &=3\, \\ \end{align}\]