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Add the following algebraic expressions :

(i) t – 4tz, 2t + 6tz
(ii) 7xy, 5xy, 3xy, – 2xy
(iii) 5x – 7y, 3y – 4x + 2, 2x – 3xy – 5
(iv) m2 – n2 – 1, n2 -1 – m2, 1 – m2 – n2
(v) 3x + 11 + 8z, 5x – 7
(vi) a2b + ab + ab2, -a2b + 2ba + 2a2b2
(vii) x – y, y – z, z – x

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(i) (t – 4tz) + (2t + 6tz) 

= t – 4tz + 2t + 6tz
= t + 2t – 4tz + 6tz
= (1 + 2)t + (-4 + 6)tz
= 31 + 212

(ii) 7xy + 5xy + 3xy – 2xy 

= (7 + 5 + 3 – 2)xy
= (15 – 2) xy
= (13)xy
= 13xy

(iii) (5x – 7y) + (3y – 4x + 2) + (2x – 3xy – 5)

= 5x – 7y + 3y – 4x + 2 + 2x – 3xy – 5
= 5x – 4x + 2x – 7y + 3y – 3xy + 2 – 5
=(5 – 4+ 2)x + (-7 + 3)y – 3xy – 3
= (7 – 4)x + (-4)y – 3xy – 3
= 3x – 4y – 3xy – 3

(iv) (m2 – n2 – 1) + (n2 – 1 – m2) + (1 – m2 – n2)

= m2 – n2 – 1 + n2 – 1 – m2 + 1 – m2 – n2
= m2 – m2 – m2 – n2 + n2 – n2 – 1 – 1 + 1
= (1 – 1 – 1)m2 + (- 1 + 1 – 1)n2 – 2 + 1
= (1 – 2)m2 + (- 2 + 1)n2 – 1
= (-1)m2 +(-1) n2 – 1
= -m2 – n2 – 1

(v) (3x + 11 + 8z) + (5x – 7)

= 3x + 11 8z + 5x – 7
= 3x + 5x + 8z + 11 – 7
= (3 + 5)x + 8z + 4
= 8x + 8z + 4

(vi) (a2b + ab + ab2) + (-a2b + 2ba + 2a2b2)

= a2b + ab + ab2 – a2b + 2ba + 2a2b2
= a2b – a2b + 2a2b2 + ab2 + ab + 2ba
= (1 – 1)a2b + 2a2b2 + ab + ab + 2ba (ab = ba)
= (0)a2b + 2a2b2 + ab2 + (1 + 2)ab
= 0 + 2a2b2 + ab2 + 3ab
= 2a2b2 + ab2 + 3ab

(vii) (x – y) + (y – z) + ( Z – x)

x – y + y – z + z – x
= x – x – y + y – z + z
= (1 – 1)x + (- 1 + 1)y + 1(-1 + 1)z
= 0x + 0y + 0z
= 0 + 0 + 0
= 0

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