Class 9, Maths, Chapter 2, Exercise 2.5, Solutions
Q.1. Use suitable identities to find the following products:
(i) (x + 4) (x + 10)
(ii) (x + 8) (x – 10)
(iii) (3x + 4) (3x – 5)
(iv) $\left( {{y}^{2}}+\frac{3}{2} \right)\left( {{y}^{2}}-\frac{3}{2} \right)$
(v) (3 – 2x) (3+2x)
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Q.2. Evaluate the following products without multiplying directly:
(i) 103 × 107
(ii) 95 × 96
(iii) 104 × 96
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Q.3. Factories the following using appropriate identities:
(i) 9x2 + 6xy + y2
(ii) 4y2 – 4y + 1
(iii) x2 – $\frac{{{y}^{2}}}{100}$
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Q.4. Expand each of the following, using suitable identities:
(i) (x + 2y + 4z)2
(ii) (2x – y + z)2
(iii) (–2x + 3y + 2z)2
(iv) (3a – 7b – c)2
(v) (–2x + 5y – 3z)2
(vi) ${{\left[ \frac{1}{4}a-\frac{1}{2}b+1 \right]}^{2}}$
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Q.5. Factories:
(i) 4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz
(ii) 2x2 + y2 + 8z2 – 2 xy + 4 yz – 8xz
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Q.6. Write the following cubes in expanded form:
(i) (2x + 1)3
(ii) (2a – 3b)3
(iii) ${{\left[ \frac{3}{2}x+1 \right]}^{3}}$
(iv) ${{\left[ x-\frac{2}{3}y \right]}^{3}}$
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Q.7. Evaluate the following using suitable identities:
(i) (99)3
(ii) (102)3
(iii) (998)3
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Q.8. Factories each of the following:
(i) 8a3 + b3 + 12a2b + 6ab2
(ii) 8a3 – b3 – 12a2b + 6ab2
(iii) 27 – 125a3 – 135a + 225a2
(iv) 64a3 – 27b3 – 144a2b + 108ab2
(v) 27p3 – $\frac{1}{216}-\frac{9}{2}{{p}^{2}}+\frac{1}{4}p$
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Q.9. Verify:
(i) x3 + y3 = (x + y) (x2 – xy + y2)
(ii) x3 – y3 = (x–y) (x2 + xy + y2)
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Q.10. Factories each of the following:
(i) 27y3 + 125z3
(ii) 64m3 – 343n3
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Q.11. Factories: 27x3 + y3 + z3 – 9xyz
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Q.12. Verify that:
x3 + y3 + z3 –3xyz = $\frac{1}{2}$ (x + y + z) [(x – y)2 + (y – z)2 + (z – x)2]
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Q.13. If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
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Q.14. Without actually calculating the cubes, find the value of each of the following:
(i) (–12)3 + (7)3 + (5)3
(ii) (28)3 + (–15)3 + (–13)3
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Q.15. Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
(i) Area: 25a2 – 35a + 12
(ii) Area: 35y2 + 13y – 12
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Q.16. What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
(i) Volume∶ 3x2 – 12x
(ii) Volume 12ky2 + 8ky – 20k
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