Selina solutions for Concise Mathematics [English] Class 9 ICSE chapter 4 - Expansions (Including Substitution) [Latest edition]

Find the square of 2a + b.

Find the square of : 3a + 7b

Find the square of : 3a - 4b

Find the square of `(3a)/(2b) - (2b)/(3a)`.

Use identities to evaluate : (101)²

Use identities to evaluate : (502)²

Use identities to evaluate : (97)²

Use identities to evaluate : (998)²

Evalute : `( 7/8x + 4/5y)^2`

Evalute : `((2x)/7 - (7y)/4)^2`

Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.

Evaluate : (4a +3b)² - (4a - 3b)² + 48ab.

If a + b = 7 and ab = 10; find a - b.

If a - b = 7 and ab = 18; find a + b.

If x + y = `7/2  "and xy" =5/2`; find:  x - y and x² - y²

If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a² - b².

If a - b = 4 and a + b = 6; find
(i) a² + b²
(ii) ab

If a + `1/a`= 6 and  a ≠ 0 find :
(i) `a - 1/a   (ii)  a^2 - 1/a^2`

If a - `1/a`= 8 and  a ≠ 0 find :
(i) `a + 1/a   (ii)  a^2 - 1/a^2`

If a² - 3a + 1 = 0, and a ≠ 0; find: 

1. `a + 1/a`         
2. `a^2 + 1/a^2`

If a² - 5a - 1 = 0 and a ≠ 0 ; find:

1. `a - 1/a`
2. `a + 1/a`
3. `a^2 - 1/a^2`

If 3x + 4y = 16 and xy = 4; find the value of 9x² + 16y².

The number x is 2 more than the number y. If the sum of the squares of x and y is 34, then find the product of x and y.

The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.

Find the cube of : 3a- 2b

Find the cube of : 5a + 3b

Find the cube of : `2a + 1/(2a)`     ( a ≠ 0 )

Find the cube of : `( 3a - 1/a )  (a ≠ 0 )`

If  a² + `1/a^2 = 47` and a ≠ 0   find :

1. `a + 1/a`
2. `a^3 + 1/a^3`

If  `a^2 + 1/a^2` = 18; a ≠ 0 find :

(i) `a - 1/a`

(ii) `a^3 - 1/a^3`

If `a + 1/a` = p and a ≠ 0; then show that:

`a^3 + 1/a^3 = p(p^2 - 3)` 

If a + 2b = 5; then show that : a³ + 8b³ + 30ab = 125.

If `( a + 1/a )^2 = 3  "and a ≠ 0; then show:"  a^3 + 1/a^3 = 0`.

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

Use property to evaluate : 13³ + (-8)³ + (-5)³

Use property to evaluate : 7³ + 3³ + (-10)³

Use property to evaluate : 9³ - 5³ - 4³

Use property to evaluate : 38³ + (-26)³ + (-12)³

If a ≠ 0 and `a - 1/a` = 3 ; find `a^2 + 1/a^2`

If a ≠ 0 and `a- 1/a` = 3 ; Find :
`a^3 - 1/a^3`

If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^2 + 1/a^2 )`

If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^4 + 1/a^4 )`

If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^3 - 1/a^3 )`

If X ≠ 0 and X + `1/"X"` = 2 ; then show that :

`x^2 + 1/x^2 = x^3 + 1/x^3 = x^4 + 1/x^4`

If 2x - 3y = 10 and xy = 16; find the value of 8x³ - 27y³.

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

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

The sum of two numbers is 9 and their product is 20. Find the sum of their (i) Squares (ii) Cubes

Two positive numbers x and y are such that x > y. If the difference of these numbers is 5 and their product is 24, find:
(i) Sum of these numbers
(ii) Difference of their cubes
(iii) Sum of their cubes.

If 4x² + y² = a and xy = b, find the value of 2x + y.

Expand : ( x + 8 ) ( x + 10 )

Expand : ( x + 8 )( x - 10 )

Expand : ( X - 8 ) ( X + 10 )

Expand : ( x - 8 )( x - 10 )

Expand : `( 2x - 1/x )( 3x + 2/x )`

Expand : `( 3a + 2/b )( 2a - 3/b )`

Expand : ( x + y - z )²

Expand : ( x - 2y + 2 )² 

Expand : ( 5a - 3b + c )²

Expand : ( 5x - 3y - 2 )²

Expand : `( x - 1/x + 5)^2`

If a + b + c = 12 and a² + b² + c² = 50; find ab + bc + ca.

If a² + b² + c² = 35 and ab + bc + ca = 23; find a + b + c.

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

If a² + b² + c² = 50 and ab + bc + ca = 47, find a + b + c.

If x+ y - z = 4 and x² + y² + z² = 30, then find the value of xy - yz - zx.

If x + 2y + 3z = 0 and x³ + 4y³ + 9z³ = 18xyz ; evaluate : 
`[( x + 2y )^2]/(xy) + [(2y + 3z)^2]/(yz) + [(3z + x)^2]/(zx)`

If a + `1/a` = m and a ≠ 0 ; find in terms of 'm'; the value of :
`a - 1/a`

If a + `1/a` = m and a ≠ 0; find in terms of 'm'; the value of `a^2 - 1/a^2`.

In the expansion of (2x² - 8) (x - 4)²; find the value of coefficient of x³.

In the expansion of (2x² - 8) (x - 4)²; find the value of coefficient of x²

In the expansion of (2x² - 8) (x - 4)²; find the value of constant term.

If x > 0 and `x^2 + 1/[9x^2] = 25/36, "Find"   x^3 + 1/[27x^3]` 

If 2( x² + 1 ) = 5x, find :
(i) `x - 1/x`

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

If a² + b² = 34 and ab = 12; find : 3(a + b)² + 5(a - b)²

If a² + b² = 34 and ab = 12; find : 7(a - b)² - 2(a + b)²

If 3x - `4/x` = 4; and x ≠ 0 find : 27x³ - `64/x^3`

If x² + `x^(1/2)`= 7 and  x ≠ 0; find the value of : 
7x³ + 8x - `7/x^3 - 8/x`

If x = `1/( x - 5 ) "and x ≠ 5. Find" : x^2 - 1/x^2`

If x = `1/[ 5 - x ]  "and x ≠ 5 find "x^3 + 1/x^3`

If 3a + 5b + 4c = 0, show that : 27a³ + 125b³ + 64c³ = 180 abc

The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their square.

Find the value of 'a':  4x² + ax + 9 = (2x + 3)²

Find the value of 'a': 4x² + ax + 9 = (2x - 3)²

Find the value of 'a': 9x² + (7a - 5)x + 25 = (3x + 5)²

If `[x^2 + 1]/x = 3 1/3  "and x > 1; Find If" x - 1/x`

If `[x^2 + 1]/x = 3 1/3  "and x > 1; Find If" x^3 - 1/x^3`

The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : Their product

The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : The sum of their squares

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

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

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)`

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]`

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

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

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

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

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

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

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