(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

Find the cube of : 5a + 3b

Find the cube of : `2a + 1/(2a)`     ( a ≠ 0 )

Find the cube of: `( 3a - 1/a )  (a ≠ 0 )`

If  a² + `1/a^2 = 47` and a ≠ 0   find :

1. `a + 1/a`
2. `a^3 + 1/a^3`

If  `a^2 + 1/a^2` = 18; a ≠ 0 find :

(i) `a - 1/a`

(ii) `a^3 - 1/a^3`

If `a + 1/a` = p and a ≠ 0; then show that:

`a^3 + 1/a^3 = p(p^2 - 3)` 

If a + 2b = 5; then show that : a³ + 8b³ + 30ab = 125.

If `( a + 1/a )^2 = 3  "and a ≠ 0; then show:"  a^3 + 1/a^3 = 0`.

If a + 2b + c = 0; then show that: a³ + 8b³ + c³ = 6abc.

Use property to evaluate : 13³ + (-8)³ + (-5)³

Use property to evaluate : 7³ + 3³ + (-10)³

Use property to evaluate : 9³ - 5³ - 4³

Use property to evaluate : 38³ + (-26)³ + (-12)³

If 4x² + y² = a and xy = b, find the value of 2x + y.

Two positive numbers x and y are such that x > y. If the difference of these numbers is 5 and their product is 24, find:

1. Sum of these numbers
2. Difference of their cubes
3. Sum of their cubes.

The sum of two numbers is 9 and their product is 20. Find the sum of their (i) Squares (ii) Cubes.

Expand : (3x + 5y + 2z) (3x - 5y + 2z)

Expand : (3x - 5y - 2z) (3x - 5y + 2z)

If 2x - 3y = 10 and xy = 16; find the value of 8x³ - 27y³.

If a ≠ 0 and `a - 1/a` = 3 ; find `a^2 + 1/a^2`