Page 153 - ICSE Math 8

2. Use a suitable identity to find the following products.
Ê 2x 3x ˆ Ê 2x 3x ˆ
4
4
4
4
(a) (5x – y)(5x – y) (b) Á 3y + 2y¯ Ë 3y + 2y¯ ˜ (c) (x – y )(x + y )
˜ Á
Ë
2 ˆ Ê
2 ˆ
3
2
2
3
2
2
3
(d) (2x + y)(2x + y) (e) (3.5x – 2.5y )(3.5x – 2.5y ) (f) Ê x + x ¯ Ë x - x ¯
3
3 ˜ Á
3 ˜
Á
Ë
3. Using a suitable identity, evaluate the following.
2
2
2
2
2
(a) (101) (b) (99) (c) (105) (d) (998) (e) (502) (f) (1,002) 2
2
2
4. Simplify the following using p – q = (p + q)(p – q).
2
2
2
2
2
(a) 38 – 12 (b) 65 ¥ 55 (c) 43 – 17 (d) 100.4 ¥ 99.6 (e) 15 – 10 2
5. Find the value of a, if:
2
(a) 12a = 50 ¥ 50 – 38 ¥ 38 (b) 23a = 68 – 45 2
6. Using suitable identities, evaluate the following.
96 9644¥ - ¥ 5275 27 0270 27. ¥ . - . ¥ .
(a) (b)
96 4- 554.
103 10333¥ - ¥ 45 45 24 51 5. ¥ . - ( .)(. ) + 1 51 5. ¥ .
(c) (d)
103 3+ 45 45 24 51 5. ¥ . + ( .)(. ) + 1 51 5. ¥ .
1 1 1
4
2
7. If x – = 5, find the values of x + and x + .
x x 2 x 4
2
2
8. Find the value of x if pqx = (3p + q) – (3p – q) .
2
9. If a + 1 = 18, find the values of a + 1 and a – 1 .
a 2 a a
2
2
10. If x – y = 6 and xy = 8, find the value of x + y .
Ê ˆ 1 2 1
2
11. If x - x¯ = 36, find the value of x + x 2 .
˜
Á
Ë
1 1
12. If p + = 12, find the value of p – .
p p
13. Find the product.
2
2
2
4
2
4
(a) (2a – 3b)(2a + 3b)(4a + 9b ) (b) (p – q)(p + q)(p + q )(p + q )
Ê 1 ˆ Ê 1 ˆ Ê 1 ˆ
2
(c) (5m – 7n)(5m + 7n) (d) Á y + y¯ Ë y - y¯ Ë y + y ¯
˜ Á
˜
˜ Á
2
Ë
14. Prove that.
2
2
(a) (x + y)(x – y) + (y + z)(y – z) + (z + x)(z – x) = 0 (b) (3x + 4y) – (3x – 4y) = 48xy
2
2
15. If x + y = 26 and xy = 3, find the value of:
4
(a) x + y (b) x – y (c) x + y 4
16. If 3x + 4y = 16 and 3x – 4y = 4, find the value of xy.
2
2
[Hint: Use the formula (p + q) – (p – q) = 4pq.]
2 1
2
2
17. Find the value of 36x + 25y – 60xy, when x = , y = .
3 5
Special Products
Special products are some special cases of products of two binomials. You have studied some of these in the
2
2
2
2
previous section, viz., (a + b) , (a – b) or a – b . Let us study a few more special products.
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