Page 102 - Start Up Mathematics_7

Example 9: Add the following algebraic expressions:

(a) 4xyz, –7xyz, 5xyz, – 3xyz (b) 3a – bc, 4bc – c, 3c – a
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(c) a + b – 3, b – a + 3, a – b + 3 (d) x – x, 1 – x + x, x + x – 1
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(e) 3p q, –2pq , –p q + 7pq 2 (f) ab – 3a, 3b – ab, 3a – 3b
Solution: (a) 4xyz – 7xyz + 5xyz – 3xyz = (4xyz + 5xyz) – (7xyz + 3xyz)
= 9xyz – 10xyz = –xyz
(b) 3a – bc + 4bc – c + 3c – a = (3a – a) + (–bc + 4bc) + (–c + 3c)
= 2a + 3bc + 2c
(c) a + b – 3 + b – a + 3 + a – b + 3

= (a – a + a) + (b + b – b) + (–3 + 3 + 3)
= a + b + 3
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(d) x – x + 1 – x + x + x + x – 1 = (x – x + x ) + (x ) + (–x + x) + (1 – 1)
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= x + x 2
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(e) 3p q – 2pq – p q + 7pq = (3p q – p q) + (–2pq + 7pq ) = 2p q + 5pq 2
(f) ab – 3a + 3b – ab + 3a – 3b = (ab – ab) + (–3a + 3a) + (3b – 3b) = 0.
Example 10: Subtract:
(a) 6xyz from –4xyz (b) p(q – 3) from q(2 – p)
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(c) –2x + 10x – 5 from 5x – 10 (d) x – x – 1 from x + x – 1
Solution: (a) –4xyz – 6xyz = –10xyz
(b) q(2 – p) – p(q – 3) = 2q – pq – pq + 3p = 2q – 2pq + 3p
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(c) (5x – 10) – (–2x + 10x – 5) = 5x – 10 + 2x – 10x + 5
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= 2x – 5x – 5
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(d) (x + x – 1) – (x – x – 1) = x + x – 1 – x + x + 1 = 2x
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Example 11: (a) What should be added to x + xy + y to obtain 3x + 4xy?
(b) What should be subtracted from 2a + 8b + 10 to get –4a + 3b + 12?
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Solution: (a) Let expression P to be added to x + xy + y to obtain 3x + 4xy.
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∴ (x + xy + y ) + P = 3x + 4xy
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⇒ P = (3x + 4xy) – (x + xy + y )
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= 3x + 4xy – x – xy – y 2
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= (3x – x ) + (4xy – xy) – y 2
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= 2x + 3xy – y 2
(b) Let Q be subtracted from (2a + 8b + 10) to get (–4a + 3b + 12).
∴ (2a + 8b + 10) – Q = (–4a + 3b + 12)
⇒ Q = (2a + 8b + 10) – (–4a + 3b + 12)
= 2a + 8b + 10 + 4a – 3b – 12
= (2a + 4a) + (8b – 3b) + (10 – 12)
= 6a + 5b – 2
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