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# (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?

**Solution:**

Let's use the concept of addition and subtraction of algebraic expressions to solve the given questions.

(a) First term = x^{2} + xy + y^{2}

Final term = 2x^{2} + 3xy

Second term = Final term - First term

= 2x^{2} + 3xy - (x^{2} + xy + y^{2})

= 2x^{2} + 3xy - x^{2} - xy - y^{2}

= x^{2} + 2xy - y^{2}

Thus, the expression to be added is x^{2} + 2xy - y^{2}

(b) Let us take the expression to be subtracted as 'X'.

2a + 8b + 10 - X = -3a + 7b + 16

X = 2a + 8b + 10 - (- 3a + 7b + 16)

X = 2a + 8b + 10 + 3a - 7b - 16

X = 5a + b - 6

Thus, the expression to be subtracted is 5a + b - 6.

**☛ Check: **NCERT Solutions for Class 7 Maths Chapter 12

**Video Solution:**

## (a) What should be added to x² + xy + y²^{ }to obtain 2x² + 3xy? (b) What should be subtracted from 2a + 8b + 10 to get - 3a + 7b + 16?

Maths NCERT Solutions Class 7 Chapter 12 Exercise 12.2 Question 4

**Summary:**

(a) x^{2} + 2xy – y^{2} should be added to x^{2} + xy + y^{2 }to obtain 2x^{2} + 3xy. (b) 5a + b − 6 should be subtracted from 2a + 8b + 10 to get -3a + 7b + 16.

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