# 3.Add the following : (i) $$ab – be, be – ca, ea – ab$$ (ii)$$a – b + ab, b-c + be, c – a + ac$$ (iii) $$2p^2q^2 – 3pq + 4, 5 + 7pq – 3p^2q^2$$ (iv)$$l^2 + m^2, m^2 + n^2, n^2 + l^2, 2lm + 2mn + 2nl$$

(i) We have the expressions as:$$ab – bc, bc – ca, ca – ab$$

$$(ab – bc) + (bc – ca) + (ca – ab)$$

$$\Rightarrow ab – bc + bc – ca + ca – ab$$

$$\Rightarrow (ab – ab) + (bc – bc) + (ca – ca)\quad$$ [Placing the like terms together]

$$\Rightarrow 0 + 0 + 0$$

$$\Rightarrow 0$$

(ii) We have the expressions as:$$a – b + ab, b – c + bc, c – a + ac$$

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

$$\Rightarrow a – b + ab + b – c + bc + c – a + ac$$

$$\Rightarrow (a – a) + (b – b) + (c – c) + ab + bc + ac\quad$$[Placing all the like terms together]

$$\Rightarrow 0 + 0 + 0 + ab + bc + ac$$

$$\Rightarrow ab + bc + ac$$

(iii)We have the expressions as:$$2p^2q^2 – 3pq + 4, 5 + 7pq – 3p^2q^2$$

Adding these we get: $$2p^2q^2 – 3pq + 4 + 5 + 7pq – 3p^2q^2$$

$$\Rightarrow (2p^2q^2– 3p^2q^2)+(– 3pq+ 7pq)+ (4 + 5)\quad$$[Placing like terms together]

$$\Rightarrow -p^2q^2 + 4pq+ 9$$

(iv)We have the expressions as:$$l^2 + m^2, m^2 + n^2, n^2 + l^2, 2lm + 2mn + 2nl$$
Adding these we get: $$(l^2 + m^2)+( m^2 + n^2)+( n^2 + l^2)+ (2lm + 2mn + 2nl)$$

$$\Rightarrow (l^2+l^2)+ (m^2+m^2)+ (n^2+n^2)+(2lm + 2mn + 2nl)\quad$$[Placing like terms together]

$$\Rightarrow (2l^2)+ (2m^2)+ (2n^2)+(2lm + 2mn + 2nl$$

$$\Rightarrow 2(l^2+ m^2+n^2+lm + mn + nl)$$