Question

(i) (2x+1) (ii) (2a-3b) (iii) \left[\frac{3}{2}x+1\right]^3 (iv) \left[x-\frac{2}{3}y\right]^3 7. Evaluate the following using suitable identities: (i) (99)^3 (ii) (102)^3 (iii) (998)^3 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-\frac{1}{216}-\frac{9}{2}p²+\frac{1}{4}p 9. Verify : (i) x³+y³=(x+y)(x²-xy+y²) (ii) x³-y³=(x-y)(x²+xy+y²) 10. Factorise each of the following: (i) 27y³+125z³ (ii) 64m³-343n³ [Hint : See Question 9.] 11. Factorise: 27x³+y³+z³-9xyz 12. Verify that x³+y³+z³-3xyz = \frac{1}{2}(x+y+z)[(x-y)²+(y-z)²+(z-x)²] 13. If x+y+z=0, show that x³+y³+z³=3xyz. 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 15. Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given: Area: 25a²-35a+12 (i) Area: 35y²+13y-12 (ii)

          (i) (2x+1)
(ii) (2a-3b)
(iii) \left[\frac{3}{2}x+1\right]^3
(iv) \left[x-\frac{2}{3}y\right]^3
7. Evaluate the following using suitable identities:
(i) (99)^3
(ii) (102)^3
(iii) (998)^3
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-\frac{1}{216}-\frac{9}{2}p²+\frac{1}{4}p
9. Verify : (i) x³+y³=(x+y)(x²-xy+y²)
(ii) x³-y³=(x-y)(x²+xy+y²)
10. Factorise each of the following:
(i) 27y³+125z³
(ii) 64m³-343n³
[Hint : See Question 9.]
11. Factorise: 27x³+y³+z³-9xyz
12. Verify that x³+y³+z³-3xyz = \frac{1}{2}(x+y+z)[(x-y)²+(y-z)²+(z-x)²]
13. If x+y+z=0, show that x³+y³+z³=3xyz.
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
15. Give possible expressions for the length and breadth of each of the following
rectangles, in which their areas are given:
Area: 25a²-35a+12
(i)
Area: 35y²+13y-12
(ii)

(i) (2x+1)
(ii) (2a-3b)
(iii) [(3)/(2)x+1]^3
(iv) [x-(2)/(3)y]^3
7. Evaluate the following using suitable identities:
(i) (99)^3
(ii) (102)^3
(iii) (998)^3
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-(1)/(216)-(9)/(2)p²+(1)/(4)p
9. Verify : (i) x³+y³=(x+y)(x²-xy+y²)
(ii) x³-y³=(x-y)(x²+xy+y²)
10. Factorise each of the following:
(i) 27y³+125z³
(ii) 64m³-343n³
[Hint : See Question 9.]
11. Factorise: 27x³+y³+z³-9xyz
12. Verify that x³+y³+z³-3xyz = (1)/(2)(x+y+z)[(x-y)²+(y-z)²+(z-x)²]
13. If x+y+z=0, show that x³+y³+z³=3xyz.
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
15. Give possible expressions for the length and breadth of each of the following
rectangles, in which their areas are given:
Area: 25a²-35a+12
(i)
Area: 35y²+13y-12
(ii)

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