English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

Factorise the following:

8a³ – b³ – 12a²b + 6ab²

Factorise the following:

27 – 125a³ – 135a + 225a²

Factorise the following:

64a³ – 27b³ – 144a²b + 108ab² 

Factorise the following:

`27p^3-1/216-9/2p^2+1/4p`

Verify:

x³ + y³ = (x + y) (x² – xy + y²)

Verify:

x³ – y³ = (x – y) (x² + xy + y²)

Factorise the following:

27y³ + 125z³

Factorise the following:

64m³ – 343n³ 

Factorise:

27x³ + y³ + z³ – 9xyz

Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`

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

Without actually calculating the cubes, find the value of the following:

(–12)³ + (7)³ + (5)³

Without actually calculating the cubes, find the value of the following:

(28)³ + (–15)³ + (–13)³

Give possible expression for the length and breadth of the following rectangle, in which their area are given:

Give possible expression for the length and breadth of the following rectangle, in which their area is given:

What are the possible expressions for the dimensions of the cuboids whose volume is given below?

What are the possible expressions for the dimensions of the cuboids whose volume is given below?

Show that in a right angled triangle, the hypotenuse is the longest side.

In the given figure sides AB and AC of ΔABC are extended to points P and Q respectively. Also, ∠PBC < ∠QCB. Show that AC > AB.

In the given figure, ∠B < ∠A and ∠C < ∠D. Show that AD < BC.