Solve the following using identities.
1. (x + 2) (x + 4)Sol. By using identity
{(x + a) (x + b) = x^2 + (a + b)x + ab }
(x + 2) (x + 4) = x^2 + (2 + 4)x + 8
= x^2 + 6x + 8
2. (x + 2) (x + 3)
Sol. By using identity
{(x + a) (x + b) = x^2 + (a + b)x + ab }
(x + 2) (x + 3) = x^2 + (2 + 3)x + 6
= x^2 + 5x + 6
3. (x + 1) (x + 4)
Sol. By using identity
{(x + a) (x + b) = x^2 + (a + b)x + ab }
(x + 1) (x + 4) = x^2 + (1 + 4)x + 4
= x^2 + 5x + 4
4. (x + 1) (x + 2)
Sol. By using identity
{(x + a) (x + b) = x^2 + (a + b)x + ab }
(x + 1) (x + 2) = x^2 + (1 + 2)x + 2
= x^2 + 3x + 2
5. (x - 1) (x + 1)
Sol. By using identity
{(x + a) (x - a) = x^2 - a^2 }
(x - 1) (x + 1) = x^2 - 1^2
= x^2 - 1
6. (x - 2) (x + 2)
Sol. By using identity
{(x + a) (x - a) = x^2 - a^2 }
(x - 2) (x + 2) = x^2 - 2^2
= x^2 - 4
7. (x - 3) (x + 3)
Sol. By using identity
{(x + a) (x - a) = x^2 - a^2 }
(x - 3) (x + 3) = x^2 - 3^2
= x^2 - 9
8. (x - 4) (x + 4)
Sol. By using identity
{(x + a) (x - a) = x^2 - a^2 }
(x - 4) (x + 4) = x^2 - 4^2
= x^2 - 16
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| maths-ncert-solution |
(100 + 1) (100 + 4)
Sol. By using identity
{(x + a) (x + b) = x^2 + (a + b)x + ab }
(100 + 1) (100 + 4) = 100^2 + (1 + 4)100 + 4
= 10000 + 500 + 4
= 10504
10. 102 * 103
(100 + 2) (100 + 3)
Sol. By using identity
{(x + a) (x + b) = x^2 + (a + b)x + ab }
(100 + 2) (100 + 3) = 100^2 + (2 + 3)100 + 6
= 10000 + 500 + 6
= 10506
11. 98 * 99
(100 - 2) (100 - 1)
Sol. By using identity
{(x + a) (x + b) = x^2 + (a + b)x + ab }
(100 - 2) (100 - 1) = 100^2 + (-2 - 1)100 + (-2 * -1)
= 10000 - 300 + 2
= 9702
12. 97 * 98
(100 - 3) (100 - 2)
Sol. By using identity
{(x + a) (x + b) = x^2 + (a + b)x + ab }
(100 - 3) (100 - 2) = 100^2 + (-3 - 2)100 + 6
= 10000 - 500 + 4
= 9504 9. 101 * 104
13. 96 * 104
(100 - 4) (100 + 4)
Sol. By using identity
{(x + a) (x - a) = x^2 - a^2 }
(100 - 4) (100 + 4) = 100^2 - 4^2
= 10000 - 16
= 9984
14. 97 * 103
(100 - 3) (100 + 3)
Sol. By using identity
{(x + a) (x - a) = x^2 - a^2 }
(100 - 3) (100 + 3) = 100^2 - 3^2
= 10000 - 9
= 9991
15. 98 * 102
(100 - 2) (100 + 2)
Sol. By using identity
{(x + a) (x - a) = x^2 - a^2 }
(100 - 2) (100 + 2) = 100^2 - 2^2
= 10000 - 4
= 9996
16. 99 * 101
(100 - 1) (100 + 1)
Sol. By using identity
{(x + a) (x - a) = x^2 - a^2 }
(100 - 1) (100 + 1) = 100^2 - 1^2
= 10000 - 1
= 9999
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