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

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`

If a ≠ 0 and `a- 1/a` = 3 ; Find :
`a^3 - 1/a^3`

If a ≠ 0 and `a - 1/a` = 4; find: `(a^2 + 1/a^2)`

If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^4 + 1/a^4 )`

If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^3 - 1/a^3 )`

If X ≠ 0 and X + `1/"X"` = 2 ; then show that :

`x^2 + 1/x^2 = x^3 + 1/x^3 = x^4 + 1/x^4`

Factorise by taking out the common factors : 
2 (2x - 5y) (3x + 4y) - 6 (2x - 5y) (x - y)

Factories by taking out common factors :
xy(3x² - 2y²) - yz(2y² - 3x²) + zx(15x² - 10y²)