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# Ex 12.2 Q6 Algebraic-Expressions Solutions NCERT Maths Class 7

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## Question

(a) From the sum of $$3x – y + 11 \text{ and } – y – 11,$$ subtract $$3x – y – 11.$$

(b) From the sum of $$4 + 3x$$ and $$5 – 4x + 2x^2,$$ subtract the sum of $$3x^2 – 5x$$ and $$-x^2 + 2x + 5$$

Video Solution
Algebraic Expressions
Ex 12.2 | Question 6

## Text Solution

What is known?

Like Terms

Reasoning:

This is based on concept identifying like terms and then performing the arithmetic operation of like terms as given in the question.

Steps:

(a) From the sum of $$3x – y + 11$$ and $$– y – 11$$, subtract $$3x – y – 11.$$

First, we add $$3x – y + 11$$ and $$– y – 11$$

\begin{align}&= {\rm{ }}3x-y + {\rm{ }}11{\rm{ }} + {\rm{ }}\left( {-y-{\rm{ }}11} \right)\\& = {\rm{ }}3x-y + {\rm{ }}11{\rm{ }}-y-{\rm{ }}11\\&= {\rm{ }}3x{\rm{ }} - 2y\end{align}

Now from $$3x – 2y$$ subtract $$3x – y – 11$$

\begin{align}&= {\rm{ }}3x{\rm{ }}-{\rm{ }}2y{\rm{ }}-{\rm{ }}\left( {3x-y-{\rm{ }}11} \right)\\&= {\rm{ }}3x{\rm{ }}-{\rm{ }}2y{\rm{ }}-{\rm{ }}3x + y + {\rm{ }}11\\&= {\rm{ }} - {\rm{ }}y{\rm{ }} + {\rm{ }}11 \end{align}

(b) From the sum of $$4 + 3x$$ and $$5 – 4x + 2x^2$$, subtract the sum of $$3x^2 – 5x$$ and  $$–x^2 + 2x + 5$$

Step 1 $$=$$ First, add $$4 + 3x$$ and $$5 – 4x + 2x^2$$

Step 2 $$=$$ Then, add $$3x^2 – 5x$$ and $$–x^2 + 2x + 5$$

Step 3 $$=$$ Subtract the resultant in step $$2$$ from resultant of step $$1$$

Steps:

Add $$4 + 3x$$ and $$5 – 4x + 2x^2$$

\begin{align}&= {\rm{ }}4{\rm{ }} + {\rm{ }}3x + {\rm{ }}5{\rm{ }}--{\rm{ }}4x + {\rm{ }}2{x^2}\\&= {\rm{ }}2{x^2} - x{\rm{ }} + {\rm{ }}9\end{align}

Now add $$3x^2 – 5x$$ and $$–x^2 + 2x + 5$$

\begin{align}&= {\rm{ }}3{x^2}-{\rm{ }}5x + \left( {{\rm{ }}-{x^2} + {\rm{ }}2x + {\rm{ }}5} \right)\\& = {\rm{ }}3{x^2}-{\rm{ }}5x--{x^2} + {\rm{ }}2x + {\rm{ }}5\\& = {\rm{ }}2{x^2}-{\rm{ }}3x{\rm{ }} + {\rm{ }}5\end{align}

Now subtract $$2x^2 – 3x + 5$$ from $$2x^2 -x + 9$$

i.e.

\begin{align}&{2{x^2} - x+ 9-\left( {2{x^2}-3x + 5} \right)}\\&=2{x^2} - x +9-2{x^2} + 3x-5\\&= 2x + 4\end{align}

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