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# Q.2 Add: (i) 3mn, -5mn, 8mn, -4mn (ii) t – 8tz, 3tz, -z, z – t (iii) -7mn + 5, 12mn + 2, 9mn – 8, -2mn – 3 (iv) a + b – 3, b – a + 3, a – b + 3 (v) 14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy (vi) 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5 (vii)$$4x^2y, -3xy^2, -5xy^2, 5x^2y$$ $$(viii) 3p^2q^2 – 4pq + 5, -10p^2q^2, 15 + 9pq + 7p^2q^2$$ (ix) ab – 4a, 4b – ab, 4a – 4b $$(x) x^2 – y^2 – 1, y^2 – 1 – x^2, 1 – x^2 – y^2$$

(i) 3mn, -5mn, 8mn, -4mn
= (3 mn) + (-5 mn) + (8 mn) + (- 4 mn)
= 3 mn - 5 mn + 8 mn - 4 mn
= 2mn
(ii) t – 8tz, 3tz – z, z – t
= t – 8tz + 3tz – z + z – t
= t – t – 8tz + 3tz – z + z
= – 5 tz
(iii) -7mn + 5, 12mn + 2, 9mn – 8, -2mn – 3
= -7mn + 5 + 12mn + 2 + 9mn – 8 + (-2mn) – 3
= -7mn + 12 mn + 9mn – 2 mn + 5 + 2 – 8 – 3
= 12 mn – 4
(iv) a + b – 3, b – a + 3, a – b + 3
= a + b – 3 + b – a + 3 + a – b + 3
= a – a + a + b + b – b – 3 + 3 + 3
= a + b + 3
(v) 14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy
= 14x + 14y – 12xy – 13 + 18 – 7x – 10y + 8xy + 4xy
= -12xy + 8xy + 4xy + 14x – 7x + 10y – 10y – 13 + 18
= 0 + 7x + 0 + 5
= 7x + 5
(vi) 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5
= 5m -7n + 3n — 4m + 2 + 2m – 3mn – 5
= 5m – 4m + 2m – 7n + 3n- 3mn + 2 – 5
= 3m – 4n – 3mn – 3
(vii)$$4x^2y, -3xy^2, -5xy^2, 5x^2y$$
= $$4x^2y + (-3xy^2) + (-5xy^2) + 5x^2y$$
=$$4x^2y + 5x^2y – 3xy^2 – 5xy^2$$
=$$9x^2y – 8xy^2$$
$$(viii) 3p^2q^2 – 4pq + 5, -10p^2q^2, 15 + 9pq + 7p^2q^2$$
$$= 3p^2q^2 – 4pq + 5 + (- 10p^2q^2) + 15 + 9pq + 7p^2q^2$$
$$= 3p^2q2 – 10p^2q^2 + 7p^2q^2 – 4pq + 9pq + 5 + 15$$
= 5pq + 20
(ix) ab – 4a, 4b – ab, 4a – 4b
= ab – 4a + (4b – ab) + (4a – 4b)
= ab – 4a + 4b – ab + 4a – 4b
= ab – ab – 4a + 4a + 4b – 4b
= 0
$$(x) x^2 – y^2 – 1, y^2 – 1 – x^2, 1 – x^2 – y^2$$
$$= x^2 – y^2 – 1 + (y^2 – 1 – x^2) + (1 – x^2 – y^2)$$
$$= x^2 – y^2 – 1 + y^2 – 1 – x^2 + 1 – x^2 – y^2$$
$$= x^2 – x^2 – x^2 – y^2 + y^2 – y^2 – 1 – 1 + 1$$
$$= -x^2 – y^2 -1$$