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

If `"r"  - (1)/"r" = 4`; find : `"r"^3 - (1)/"r"^3`

If `"a"  + (1)/"a" = "p"`; then show that `"a"^3 + (1)/"a"^3 = "p"("p"^2 - 3)`

If `("a" + 1/"a")^2 = 3`; then show that `"a"^3 + (1)/"a"^3 = 0`

If a + b + c = 0; then show that a³ + b³ + c³ = 3abc.

If a + 2b + c = 0; then show that a³ + 8b³ + c³ = 6abc

If x³ + y³ = 9 and x + y = 3, find xy.

If a + b = 5 and ab = 2, find a³ + b³.

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