Page 113 - Start Up Mathematics_8 (Non CCE)

Thinking Skills

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1. Using the identity (a + b + c) = a + b + c + 2ab + 2bc + 2ca, evaluate the following:
Ê 1 3 ˆ 2
(a) (2x – 5y + 7z) 2 (b) Á -5a + 2 b + 4 c ˜ (c) (–2x + y – 8z) 2
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2. Simplify the following:
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(a) (a – b + c) – (a – b – c) (b) (–2x – 3y + 5z) – (2x + 3y – 5z) 2
Some NCERT Textbook Questions
1. Add the following
(i) ab – bc, bc – ca, ca – ab (ii) a – b + ab, b – c + bc, c – a + ac
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2 2
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2 2
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(iii) 2p q – 3pq + 4, 5 + 7pq – 3p q (iv) l + m , m + n , n + l , 2lm + 2mn + 2nl
2. (a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3
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(b) Subtract 4p q – 3pq + 5pq – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq + 5p q
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3. (a) Simplify 3x(4x – 5) + 3 and find its values for (i) x = 3 (ii) x = .
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(b) Simplify a(a + a + 1) + 5 and find its value for (i) a = 0, (ii) a = 1 (iii) a = –1.
4. Simplify
(i) (a + b)(c – d) + (a – b)(c + d) + 2(ac + bd)
(ii) (x + y)(2x + y) + (x + 2y)(x – y)
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(iii) (x + y)(x – xy + y )
(iv) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y
5. Simplify
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2 2
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(i) (a – b ) (ii) (2x + 5) – (2x – 5) (iii) (7m – 8n) + (7m + 8n) 2
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(iv) (4m + 5n) + (5m + 4n) (v) (2.5p – 1.5q) – (1.5p – 2.5q) (vi) (ab + bc) – 2ab c
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3 2
(vii) (m – n m) + 2m n
6. Show that:
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(i) (3x + 7) – 84x = (3x – 7) 2
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(ii) Ê 4 m - 3 ˆ ˜ 2 + 2mn = 16 m + 16 n 2
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(iii) (a – b)(a + b) + (b – c)(b + c) + (c – a)(c + a) = 0
7. Using identities, evaluate.
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(i) 102 (ii) 998 (iii) 78 × 82 (iv) 1.05 × 9.5
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8. Using (x + a)(x + b) = x + (a + b)x + ab, find
(i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8
Exemplar Problems
1. Sum of a – b + ab, b + c – bc and c – a – ac is:
(a) 2c + ab – ac – bc (b) 2c – ab – ac – bc
(c) 2c + ab + ac + bc (c) 2c – ab + ac + bc
2. Volume of a rectangular box with l = b = h = 2x is ___________.
3. The product of one negative and one positive term is a negative term. (True/False)
2 2
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2 2
2 2
2 2
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4. Subtract 2ab c + 4a b c – 5a bc from –10a b c + 4ab c +2a bc .
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5. Subtract b(b + b – 7) + 5 from 3b – 8 and find the value of expression obtained for b = –3.
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