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

Factorise the following by taking out the common factors:
(mx + ny)² + (nx - my)²

Factorise the following by taking out the common factors:
36(x + y)³ - 54(x + y)²

Factorise the following by taking out the common factors:
p(p² + q² - r²) + q(r² - q² -p²) - r(p² + q² - r²)

Factorise:

`y^2 + (1)/(4y^2) + 1 - 6y - (3)/y`

Factorise:

`4"a"^2 + (1)/(4"a"^2) - 2 - 6"a" + (3)/(2"a")`

Factorise:
x⁴ + y⁴ - 6x²y²

Factorise:
4x⁴ + 25y⁴ + 19x²y²

Factorise:

`"p"^2 + (1)/"p"^2 - 3`

Factorise:
5x² - y² - 4xy + 3x - 3y

Solve the following simultaneous equations :
6x + 3y = 7xy
3x + 9y = 11xy

Solve the following simultaneous equation :
8v - 3u = 5uv
6v - 5u = -2uv

Solve the following simultaneous equations :
3(2u + v) = 7uv
3(u + 3v) = 11uv

Solve the following simultaneous equations :
2(3u - v) = 5uv
2(u + 3v) = 5uv

Solve the following simultaneous equations:
13a - 11b = 70
11a - 13b = 74

Solve the following simultaneous equations:
41x + 53y = 135
53x + 41y = 147

Solve the following simultaneous equations:
65x - 33y = 97
33x - 65y = 1

Solve the following simultaneous equations:
103a + 51b = 617
97a + 49b = 583

Solve the following pairs of equations:

`(3)/(5) x - (2)/(3) y + 1` = 0

`(1)/(3) y + (2)/(5) x ` = 4

Solve the following pairs of equations:

`x/(3) + y/(4)` = 11

`(5x)/(6) - y/(3)` = -7

Solve the following pairs of equations:

`(3)/(2x) + (2)/(3y)` = 5

`(5)/x - (3)/y` = 1