Frank solutions for Mathematics [English] Class 9 ICSE chapter 4 - Expansions [Latest edition]

Expand the following:
(a + 4) (a + 7)

Expand the following:
(m + 8) (m - 7)

Expand the following:
(x - 5) (x - 4)

Expand the following:
(3x + 4) (2x - 1)

Expand the following:
(2x - 5) (2x + 5) (2x- 3)

Expand the following:
(a + 3b)²

Expand the following:
(2p - 3q)²

Expand the following:

`(2"a" + 1/(2"a"))^2`

Expand the following:
(x - 3y - 2z)²

Find the squares of the following:
9m - 2n

Find the squares of the following:
3p - 4q²

Find the squares of the following:

`(7x)/(9y) - (9y)/(7x)`

Find the squares of the following: 
(2a + 3b - 4c)

Simplify by using formula :
(5x - 9) (5x + 9)

Simplify by using formula :
(2x + 3y) (2x - 3y)

Simplify by using formula :
(a + b - c) (a - b + c)

Simplify by using formula :
(x + y - 3) (x + y + 3)

Simplify by using formula :
(1 + a) (1 - a) (1 + a²)

Simplify by using formula :

`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`

Evaluate the following without multiplying:
(95)²

Evaluate the following without multiplying:
(103)²

Evaluate the following without multiplying:
(999)²

Evaluate the following without multiplying:
(1005)²

Evaluate, using (a + b)(a - b)= a² - b².
399 x 401

Evaluate, using (a + b)(a - b)= a² - b².
999 x 1001

Evaluate, using (a + b)(a - b)= a² - b².
4.9 x 5.1

Evaluate, using (a + b)(a - b)= a² - b².
15.9 x 16.1

If a - b = 10 and ab = 11; find a + b.

If x + y = 9, xy = 20
find: x - y

If x + y = 9, xy = 20
find: x² - y².

If `"a"  + 1/"a" = 6;`find `"a"  - 1/"a"`

If `"a"  + 1/"a" = 6;`find `"a"^2 - 1/"a"^2`

If `"a"  - 1/"a" = 10;` find `"a"  + 1/"a"`

If `"a"  - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`

If `x + (1)/x = 3`; find `x^2 + (1)/x^2`

If `x + (1)/x = 3`; find `x^4 + (1)/x^4`

If p + q = 8 and p - q = 4, find:
pq

If p + q = 8 and p - q = 4, find:
p² + q²

If m - n = 0.9 and mn = 0.36, find:
m + n

If m - n = 0.9 and mn = 0.36, find:
m² - n².

If x + y = 1 and xy = -12; find:
x - y

If x + y = 1 and xy = -12; find:
x² - y².

If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :

`"a"  + (1)/"a"`

If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :

`"a"^2 + (1)/"a"^2`

If a² - 3a - 1 = 0 and a ≠ 0, find : `"a"  - (1)/"a"`

If a² - 3a - 1 = 0 and a ≠ 0, find : `"a"  + (1)/"a"`

If a² - 3a - 1 = 0 and a ≠ 0, find : `"a"^2 - (1)/"a"^2`

If 2x + 3y = 10 and xy = 5; find the value of 4x² + 9y²

If x + y + z = 12 and xy + yz + zx = 27; find x² + y² + z².

If a² + b² + c² = 41 and a + b + c = 9; find ab + bc + ca.

If p² + q² + r² = 82 and pq + qr + pr = 18; find p + q + r.

If x + y + z = p and xy + yz + zx = q; find x² + y² + z².

Find the cube of: 2a - 5b

Find the cube of: 4x + 7y

Find the cube of: `3"a" + (1)/(3"a")`

Find the cube of: `4"p" - (1)/"p"`

Find the cube of: `(2"m")/(3"n") + (3"n")/(2"m")`

Find the cube of: `"a"  - (1)/"a" + "b"`

If `5x + (1)/(5x) = 7`; find the value of `125x^3 + (1)/(125x^3)`.

If `3x - (1)/(3x) = 9`; find the value of `27x^3 - (1)/(27x^3)`.

If `x + (1)/x = 5`, find the value of `x^2 + (1)/x^2, x^3 + (1)/x^3` and `x^4 + (1)/x^4`.

If `"a"  - (1)/"a" = 7`, find `"a"^2 + (1)/"a"^2 , "a"^2 - (1)/"a"^2` and `"a"^3 - (1)/"a"^3`

If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a"  + (1)/"a"`

If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a"^3 + (1)/"a"^3`

If `"m"^2 + (1)/"m"^2 = 51`; find the value of `"m"^3 - (1)/"m"^3`

If `9"a"^2 + (1)/(9"a"^2) = 23`; find the value of `27"a"^3 + (1)/(27"a"^3)`

If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x` 

If `x^2 + (1)/x^2 = 18`; find : `x^3 - (1)/x^3`

If `"p"  + (1)/"p" = 6`; find : `"p"^2 + (1)/"p"^2`

If `"p"  + (1)/"p" = 6`; find : `"p"^4 + (1)/"p"^4`

If `"p"  + (1)/"p" = 6`; find : `"p"^3 + (1)/"p"^3`

If `"r"  - (1)/"r" = 4`; find: `"r"^2 + (1)/"r"^2`

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

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

If `"a" + (1)/"a" = 2`, then show that `"a"^2 + (1)/"a"^2 = "a"^3 + (1)/"a"^3 = "a"^4 + (1)/"a"^4`

If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.

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:
(4x + 5y)² + (4x - 5y)²

Simplify:
(7a +5b)² - (7a - 5b)²

Simplify:
(a + b)³ + (a - b)³

Simplify:

`("a" - 1/"a")^2 + ("a" + 1/"a")^2`

Simplify:
(x + y - z)² + (x - y + z)²

Simplify:

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

Simplify:
(2x + y)(4x² - 2xy + y²)

Simplify:

`(x - 1/x)(x^2 + 1 + 1/x^2)`

Simplify:
(x + 2y + 3z)(x² + 4y² + 9z² - 2xy - 6yz - 3zx)

Simplify:
(1 + x)(1 - x)(1 - x + x²)(1 + x + x²)

Simplify:
(3a + 2b - c)(9a² + 4b² + c² - 6ab + 2bc +3ca)

Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)

Simplify:
(2x - 4y + 7)(2x + 4y + 7)

Simplify:
(3a - 7b + 3)(3a - 7b + 5)

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 

Evaluate the following :
7.16 x 7.16 + 2.16 x 7.16 + 2.16 x 2.16

Evaluate the following :
1.81 x 1.81 - 1.81 x 2.19 + 2.19 x 2.19