# Ex 12.2 Q4 Algebraic-Expressions Solutions NCERT Maths Class 7

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## Question

(a) What should be added to $$x^2 + xy + y^2$$ to obtain $$2x^2 + 3xy?$$

(b) What should be subtracted from $$2a + 8b + 10$$ to get $$– 3a + 7b + 16?$$

## Text Solution

What is known?

We know that arithmetic operation will be applied.

Reasoning:

In this question basic concept of arithmetic operations is applied. We are given two terms and asked what should be added to one term to get the required answer. For this we will subtract the first term from the answer to get what should be added. E.g. what should be added to $$3$$ to get $$5.$$ We will subtract $$3$$ from $$5.$$

Steps:

1st term $$=x^2 + xy + y^2$$

Answer term $$= 2x^2 + 3xy$$

2nd term $$=$$ Answer term $$-$$ 1st term

2nd term

\begin{align}&= 2x^2 + 3xy – (x^2 + xy + y^2)\\&= 2{x^2} + {\rm{ }}3xy{\rm{ }}-{\rm{ }}{x^2} - xy{\rm{ }} - {\rm{ }}{y^2}\\&= {x^{2{\rm{ }} + }}2xy{\rm{ }} - {y^2}\end{align}

So, $$x^2 + 2xy - y^2$$ should be added to $$x^2 + xy + y^2$$ to obtain $$2x^2 + 3xy$$

(b) What should be subtracted from $$2a + 8b + 10$$ to get $$–3a + 7b + 16?$$

What is known?

We know that arithmetic operation will be applied.

Reasoning:

In this question basic concept of arithmetic operations is applied. We are given two terms and asked what should be subtracted from one term to get the required answer. For this we will subtract the given answer from the 1st term to get what should be subtracted. E.g: what should be subtracted from $$5$$ to get $$3.$$ We will subtract $$3$$ from $$5.$$

Steps:

1st term $$= 2a + 8b + 10$$

Answer term $$= \,– 3a + 7b + 16$$

2nd term = 1st term - Answer

2nd term

\begin{align}&= \rm{}2a + 8b + 10 – (– 3a + 7b + 16)\\&= {\rm{ }}2a + {\rm{ }}8b + {\rm{ }}10{\rm{ }} + {\rm{ }}3a - {\rm{ }}7b - {\rm{ }}16\\&= 5a{\rm{ }} + {\rm{ }}b{\rm{ }} - {\rm{ }}6\end{align}

So, $$5a + b – 6$$ should be subtracted from $$2a + 8b + 10$$ to obtain $$– 3a + 7b + 16$$

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