1.

Find the sum of the following expressions (i) 7p + 6q, 5p – q, q + 16p(ii) a + 5b + 7c, 2a + 106 + 9c(iii) mn + t, 2mn – 2t, – 3t + 3mn(iv) u + v, u – v, 2u + 5v, 2u – 5v(v) 5xyz – 3xy, 3zxy – 5yx

Answer»

(i) (7p + 6q) + (5p – q) + (q + 16p) = 7p + 6q + 5p – q + q + 16p

= (7p + 5p + 16p) + (6q – q + q)

= (7 + 5 + 16)p + (6 – 1 + 1)q

= (12 + 16)p + 6q = 28p + 6q

(ii) (a + 5b + 7c) + (2a + 10b + 9c) = a + 5b + 7c + 2a + 10b + 9c

= a + 2a + 5b + 10b + 7c + 9c

= (1 + 2)a + (5 + 10)b + (7 + 9)c

= 3a + 15b + 16c

(iii) (mn + t) + (2mn – 2t) + (-3t + 3mn)

= mn + t + 2mn – 2t + (-3t) + 3mn

= (mn + 2mn + 3mn) + (t – 2t – 3t)

= (1 + 2 + 3)mn + (1 – 2 – 3)t

= 6mn + (1 – 5)t

= 6mn + (- 4)t

= 6mn – 4t

(iv) (u + v) + (u – v) + (2u + 5v) + (2u – 5v)

= u + v + u – v + 2u + 5v + 2u – 5v

= u + u + 2u + 2u + v – v + 5v – 5v

= (1 + 1 + 2 + 2)u + (1 – 1 + 5 – 5)v = 6u + 0v

= 6u

(v) 5xyz – 3xy + 3zxy – 5yx = 5xyz + 3xyz – 3xy – 5xy

= (5 + 3)xyz + [(-3) + (-5)]xy = 8xyz + (-8)xy

= 8xyz – 8xy



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