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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) \(- 2{p^3} - 3{p^2} + 4p + 7\)

 Video Solution
Algebraic Expressions
Ex 12.3 | Question 2

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) \(- 2{p^3} - 3{p^2} + 4p + 7\)

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