# Add the following

(i) ab - bc, bc - ca, ca - ab

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

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

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

**Solution:**

The given algebraic expressions are written by rearranging and combining like terms followed by performing the addition operation as follows:

(i) (ab – bc) + (bc – ca) + (ca - ab)

= ab – bc + bc – ca + ca – ab

= ab – ab – bc + bc – ca + ca

= 0

Thus, the sum of the given expressions is 0.

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

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

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

= 0 + 0 + 0 + ab + bc + ca

= ab + bc + ca

Thus, the sum of the given expressions is ab + bc + ac .

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

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

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

= – p^{2}q^{2} + 4pq + 9

Thus, the sum of the given expressions is - p^{2}q^{2} + 4pq + 9.

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

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

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

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

Thus, the sum of the given expressions is 2(l^{2} + m^{2} + n^{2} + lm + mn + nl ).

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 9

**Video Solution:**

## Add the following. (i) ab - bc, bc - ca, ca - ab (ii) a - b + ab, b - c + bc , c - a + ac (iii) 2 p²q² - 3 pq + 4, 5 + 7 pq - 3 p²q² (iv) l² + m², m² + n², n² + l², 2lm + 2mn + 2nl

Maths NCERT Solutions Class 8 Chapter 9 Exercise 9.1 Question 3

**Summary:**

The sum of the given expressions (i) ab - bc, bc - ca, ca - ab (ii) a - b + ab, b - c + bc , c - a + ac (iii) 2 p^{2}q^{2} - 3 pq + 4, 5 + 7 pq - 3 p^{2}q^{2v}(iv) l^{2} + m^{2}, m^{2} + n^{2}, n^{2} + l^{2}, 2lm + 2mn + 2nl are (i) 0 (ii) ab + bc + ac (iii) -p^{2}q^{2} + 4pq + 9 (iv) 2(l^{2} + m^{2} + n^{2} + lm + mn + nl )

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