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

If p - q = -1 and pq = -12, find p³ - q³

If m - n = -2 and m³ - n³ = -26, find mn.

If 2a - 3b = 10 and ab = 16; find the value of 8a³ - 27b³.

If x + 2y = 5, then show that x³ + 8y³ + 30xy = 125.

Simplify:
(a + b)³ + (a - b)³

Simplify:

`("a" + 1/"a")^3 - ("a" - 1/"a")^3`

Evaluate the following :
(3.29)³ + (6.71)³ 

Evaluate the following :
(5.45)³ + (3.55)³ 

Evaluate the following :
(8.12)³ - (3.12)³ 

Factorise the following by taking out the common factors:
4x²y³ - 6x³y² - 12xy²

Factorise the following by taking out the common factors:
5a(x² - y²) + 35b(x² - y²)

Factorise the following by taking out the common factors:
2x⁵y + 8x³y² - 12x²y³

Factorise the following by taking out the common factors:
12a³ + 15a²b - 21ab²

Factorise the following by taking out the common factors:
24m⁴n⁶ + 56m⁶n⁴ - 72m²n²

Factorise the following by taking out the common factors:
(a - b)² -2(a - b)

Factorise the following by taking out the common factors:
2a(p² + q²) + 4b(p² + q²)

Factorise the following by taking out the common factors:
81(p + q)² -9p - 9q

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)