Numerical Problems with Answers, Solution | Algebra | Maths - Exercise 3.4 : Algebraic Identities | 9th Maths : UNIT 3 : Algebra
Chapter: 9th Maths : UNIT 3 : Algebra
Exercise 3.4 : Algebraic Identities
Exercise 3.4 : Algebraic
Identities
1. Expand the following:
(i) (x + 2y + 3z)2 (ii) (−p + 2q + 3r)2 (iii) (2 p + 3)(2 p − 4)(2 p −5) (iv) (3a + 1)(3a −2)(3a + 4)
2. Using algebraic identity, find the
coefficients of x2 , x and constant term without actual
expansion.
(i) (x + 5)(x
+ 6)(x
+ 7) (ii)
(2x
+ 3)(2x
−5)(2x
−6)
3. If (x + a
)(x +b)(x + c
) = x3 + 14x2
+ 59x
+ 70
, find the value of
(i) a + b +c (ii) 1/a + 1/b + 1/c (iii) a2 + b2 +c2 (iv) a/bc +
b/ac + c/ab
4. Expand:
(i) (3a − 4b)3 (ii) ( x
+ 1/y )3
5. Evaluate the following by using identities:
(i) 983 (ii) 10013
6. If (x + y
+ z)
= 9 and (xy + yz + zx)
= 26,
then find the value of x2 + y2 + z
2 .
7. Find 27a 3 + 64b3,
if 3a + 4b = 10
and ab = 2 .
8. Find x 3 -y3 , if
x − y = 5 and
xy = 14 .
9. If a + 1/a = 6 , then find the
value of a3 + 1/a3 .
10. If x2 + [1/x2]
= 23 , then find the value of x + [1/x] and x3 + [1/ x3].
11. If (y – 1/y)3 = 27
, then find the value of y3 – [1/y3]
12. Simplify: (i) (2a + 3b
+ 4c
)(4a2 + 9b2 +16c
2 − 6ab −12bc
− 8ca)
(ii) (x − 2y
+ 3z
)(x 2 + 4y 2 + 9z
2 + 2xy + 6yz
− 3xz)
13. By using identity evaluate the following:
(i) 73 − 103 +
33 (ii) 1 + 1/8 – 27/8
14. If 2x − 3y
− 4z
= 0 ,
then find 8x 3 − 27y3 − 64z 3.
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