Solve the following using identities (Part-5)
1. (x + 1)^3
Sol. Using the identity
(a + b)^3 = a^3 + b^3 + 3 a b (a + b)
(x + 1)^3
x^3 + 1^3 + 3 x (x + 1)
x^3 + 1 + 3 x^2 + 3 x
x^3 + 3 x^2 + 3 x + 1
2. (x + 2)^3
Sol. Using the identity
(a + b)^3 = a^3 + b^3 + 3 a b (a + b)
(x + 2)^3
x^3 + 2^3 + 3 * x * 2 (x + 2)
x^3 + 8 + 6 x^2 + 12 x
x^3 + 6 x^2 + 12 x + 8
3. (x/2 + 2)^3
Sol. Using the identity
(a + b)^3 = a^3 + b^3 + 3 a b (a + b)
(x/2 + 2)^3
(x/2)^3 + 2^3 + 3 * x/2 * 2 (x/2 + 2)
(x^3)/8 + 8 + 3 * x^2/2 + 6 x
x^3 + (3 x^2)/2 + 6 x + 8
4. (3x + 4)^3
Sol. Using the identity
(a + b)^3 = a^3 + b^3 + 3 a b (a + b)
(3x + 4)^3
(3x)^3 + 4^3 + 3 * 3 x * 4 (3x + 4)
27 x^3 + 64 + 108 x^2 + 144 x
27 x^3 + 108 x^2 + 144 x + 64
5. (101)^3
Sol. Using the identity
(a + b)^3 = a^3 + b^3 + 3 a b (a + b)
(100 + 1)^3
100^3 + 1^3 + 3 * 100 * 1 (100 + 1)
1000000 + 1 + 300 * 101
1000000 + 30300 + 1
1030301
6. (102)^3
Sol. Using the identity
(a + b)^3 = a^3 + b^3 + 3 a b (a + b)
(100 + 2)^3
100^3 + 2^3 + 3 * 100 * 2 (100 + 2)
1000000 + 8 + 600 * 102
1000000 + 61200 + 8
1061208
7. (103)^3
Sol. Using the identity
(a + b)^3 = a^3 + b^3 + 3 a b (a + b)
(100 + 3)^3
100^3 + 3^3 + 3 * 100 * 3 (100 + 3)
1000000 + 27 + 900 * 103
1000000 + 92700 + 27
1092727
8. (104)^3
Sol. Using the identity
(a + b)^3 = a^3 + b^3 + 3 a b (a + b)
(100 + 4)^3
100^3 + 4^3 + 3 * 100 * 4 (100 + 4)
1000000 + 64 + 1200 * 104
1000000 + 124800 + 64
1124864
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| maths-ncert-solution |
Sol. Using the identity
(a - b)^3 = a^3 - b^3 - 3 a b (a - b)
(x - 1)^3
x^3 - 1^3 - 3 x (x - 1)
x^3 - 1 - 3 x^2 - 3 x
x^3 - 3 x^2 - 3 x - 1
10. (x - 2)^3
Sol. Using the identity
(a - b)^3 = a^3 - b^3 - 3 a b (a - b)
(x - 2)^3
x^3 - 2^3 - 3 * x * 2 (x - 2)
x^3 - 8 - 6 x^2 - 12 x
x^3 - 6 x^2 - 12 x - 8
11. (x/2 - 2)^3
Sol. Using the identity
(a - b)^3 = a^3 - b^3 - 3 a b (a - b)
(x/2 - 2)^3
(x/2)^3 - 2^3 - 3 * x/2 * 2 (x/2 - 2)
(x^3)/8 - 8 - 3 * x^2/2 - 6 x
x^3 - (3 x^2)/2 - 6 x - 8
12. (3x - 4)^3
Sol. Using the identity
(a - b)^3 = a^3 - b^3 - 3 a b (a - b)
(3x - 4)^3
(3x)^3 - 4^3 - 3 * 3 x * 4 (3x - 4)
27 x^3 - 64 - 108 x^2 - 144 x
27 x^3 - 108 x^2 - 144 x - 64
13. (99)^3
Sol. Using the identity
(a - b)^3 = a^3 - b^3 - 3 a b (a - b)
(100 - 1)^3
100^3 - 1^3 - 3 * 100 * 1 (100 - 1)
1000000 - 1 - 300 * 99
1000000 – 29700 – 1 = 1000000 - 29701
970299
14. (98)^3
Sol. Using the identity
(a - b)^3 = a^3 - b^3 - 3 a b (a - b)
(100 - 2)^3
100^3 - 2^3 - 3 * 100 * 2 (100 - 2)
1000000 - 8 - 600 * 98
1000000 – 58800 – 8 = 1000000 - 58808
941192
15. (97)^3
Sol. Using the identity
(a - b)^3 = a^3 - b^3 - 3 a b (a - b)
(100 - 7)^3
100^3 - 3^3 - 3 * 100 * 3 (100 - 3)
1000000 - 27 - 900 * 97
1000000 – 87300 – 27 = 1000000 – 87327
912700
16. (96)^3
Sol. Using the identity
(a - b)^3 = a^3 - b^3 - 3 a b (a - b)
(100 - 4)^3
100^3 - 4^3 - 3 * 100 * 4 (100 - 4)
1000000 - 64 - 1200 * 96
1000000 – 115200 – 64 = 1000000 - 115264
884736
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