**.**

**NCERT Solutions for Class 8 Maths Chapter 8 ****Algebraic Expressions and Identities**** Ex 8.1**

**Ex 8.1 Class 8 Maths Question 1.**

### Add the following.

(i) ab – bc, bc – ca, ca – ab

(ii) a – b + ab, b – c + bc, c – a + ac

(iii) 2p^{2}q^{2} – 3pq + 4, 5 + 7pq – 3p^{2}q^{2}

(iv) l^{2} + m^{2}, m^{2} + n^{2}, n^{2} + l^{2}, 2lm + 2mn + 2nl

**Solution:**(i) Given algebraic expressions are ab – bc, bc – ca, ca – ab

We have,

(ab – bc) + (bc – ca) + (ca – ab) (Adding all the terms)

= ab – bc + bc – ca + ca – ab

= (ab – ab) + (bc – bc) + (ca – ca) (Collecting the like terms together)

= 0 + 0 + 0

= 0

(ii) Given algebraic expressions are

a – b + ab, b – c + bc, c – a + ac

We have,

(a – b + ab) + (b – c + bc) + (c – a + ac) (Adding all the terms)

= a – b + ab + b – c + bc + c – a + ac

= (a – a) + (b – b) + (c – c) + ab + bc + ac (Collecting all the like terms together)

= 0 + 0 + 0 + ab + bc + ac

= ab + bc + ac

(iii) Given algebraic expressions are

2p^{2}q^{2} – 3pq + 4, 5 + 7pq – 3p^{2}q^{2}

By arranging the like terms in the same column, we get

(iv) Given algebraic expressions are

l^{2} + m^{2}, m^{2} + n^{2}, n^{2} + l^{2}, 2lm + 2mn + 2nl

By arranging the like terms in the same column, we get

2(l^{2} + m^{2} + n^{2} + lm + mn + nl)

**Ex 8.1 Class 8 Maths Question 2.**

### (a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3

(6) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

(c) Subtract 4p^{2}q – 3pq + 5pq^{2} – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq^{2} + 5p^{2}q

**Solution:**(a) Arranging the like terms column-wise, we get

(b) Arranging the like terms column-wise, we get

[Changing the signs of all the terms of lower expressions and then add]

(c) Arranging the like terms column-wise, we get

[Changing the signs of all the terms of lower expressions and then add]

**Related Links:**

**NCERT Solutions for Maths Class 9**

**NCERT Solutions for Maths Class 10**

**NCERT Solutions for Maths Class 11**