English Medium कक्षा ९ - CBSE Question Bank Solutions

Factorise:

`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`

Write the following cube in expanded form:

(2x + 1)³ 

Write the following cube in expanded form:

(2a – 3b)³

Write the following cube in expanded form:

`[3/2x+1]^3`

Write the following cube in expanded form:

`[x-2/3y]^3`

Evaluate the following using suitable identity:

(99)³ 

Evaluate the following using suitable identity:

(102)³ 

Evaluate the following using suitable identity:

(998)³ 

Factorise the following:

8a³ + b³ + 12a²b + 6ab²

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.