(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?

Solution:

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

(a) First term = x² + xy + y²

Final term = 2x² + 3xy

Second term = Final term - First term

= 2x² + 3xy - (x² + xy + y²)

= 2x² + 3xy - x² - xy - y²

= x² + 2xy - y²

Thus, the expression to be added is x² + 2xy - y²

(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) x² + 2xy – y² should be added to x² + xy + y² to obtain 2x² + 3xy. (b) 5a + b − 6 should be subtracted from 2a + 8b + 10 to get -3a + 7b + 16.

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