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

Simplify : ( x - 6 )( x - 4 )( x - 2 )

Simplify: (x + 6) (x − 4) (x − 2)

Simplify using following identity : `( a +- b )(a^2 +- ab + b^2) = a^3 +- b^3`
( 2x + 3y )( 4x² + 6xy + 9y² )

Simplify using following identity : `( a +- b )(a^2 +- ab + b^2) = a^3 +- b^3`
`( 3x - 5/x )( 9x^2 + 15 + 25/x^2)`

Simplify using following identity : `( a +- b )(a^2 +- ab + b^2) = a^3 +- b^3`
`(a/3 - 3b)(a^2/9 + ab + 9b^2)`

Find : (a + b)(a + b)

Find : (a + b)(a + b)(a + b)

Find : (a - b)(a - b)(a - b)

Prove that :  x²+ y² + z² - xy - yz - zx  is always positive.

If a + b = 11 and a² + b² = 65; find a³ + b³.

If x = 3 + 2√2, find :
(i) `1/x`

(ii) `x - 1/x`

(iii) `( x - 1/x )^3`

(iv) `x^3 - 1/x^3`

If x + 5y = 10; find the value of x³ + 125y³ + 150xy − 1000.

If a − 2b + 3c = 0; state the value of a³ − 8b³ + 27c³.

Using suitable identity, evaluate (104)³

Using suitable identity, evaluate (97)³ 

Simplify :
`[(x^2 - y^2)^3 + (y^2 - z^2)^3 + (z^2 - x^2)^3]/[(x - y)^3 + (y - z)^3 + (z - x)^3]`

Evaluate :
`[0.8 xx 0.8 xx 0.8 + 0.5 xx 0.5 xx 0.5]/[0.8 xx 0.8 - 0.8 xx 0.5 + 0.5 xx .5]`

Evaluate :
`[1.2 xx 1.2 + 1.2 xx 0.3 + 0.3 xx 0.3 ]/[ 1.2 xx 1.2 xx 1.2 -  0.3 xx 0.3 xx 0.3]`

Factorise by the grouping method : a³ + a - 3a² - 3

Factorise by the grouping method: 16 (a + b)² - 4a - 4b