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NCERT SOLUTIONS CLASS 9 MATHEMATICS

Exercise 2.5

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) (y2+ 32) (y2 - 32)

(v) (3 - 2x) (3 + 2x)

Q.2. Evaluate the following products without multiplying directly:

(i) 103 × 107 (ii) 95 × 96 (iii) 104 × 96

Q.3. Factorise the following using appropriate identities:

(i) 9x2 + 6xy + y(ii) 4y2 - 4y + 1  (iii) x- y2100

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) [14 a - 12 b + 1]2

Q.5. Factorise:

(i) 4x2 + 9y2 + 16z2 + 12xy - 24yz - 16xz

(ii) 2x2 + y2 + 8z2 - 2√2 xy + 4√2 yz - 8xz

Q.6. Write the following cubes in expanded form:

(i) (2x + 1)3 (ii) (2a - 3b)3 (iii) [32 x + 1]3 (iv) [x - 23 y]3

Q.7. Evaluate the following using suitable identities:

(i) (99)3 (ii) (102)3 (iii) (998)3

Q.8. Factorise 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 -1216-92p2 + 14p

Q.9. Verify:

(i) x3 + y3 = (x + y) (x2 - xy + y2)

(ii) x3 - y3 = (x - y) (x2 + xy + y2)

Q.10. Factorise each of the following:

(i) 27y3 + 125z3 (ii) 64m3 - 343n3

Q.11. Factorise: 27x3 + y3 + z3 - 9xyz

Q.12. Verify that: x3 + y3 + z3 - 3xyz = 12(x + y + z) [(x - y)+ (y - z)+ (z - x)2]

Q.13. If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.

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

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: 35 y2 + 13y - 12

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