Selina solutions for Concise Mathematics [English] Class 8 ICSE chapter 11 - Algebraic Expressions [Latest edition]

Separate the constants and variables from the following :

`-7,7+"x",7"x"+"yz",sqrt5,sqrt("xy"),(3"yz")/8,4.5"y"-3"x",`

8 −5, 8 − 5x, 8x −5y × p and 3y²z ÷ 4x

Write the number of the term of the following polynomial.

5x² + 3 x ax

Write the number of the term of the following polynomial.

ax ÷ 4 – 7

Write the number of the term of the following polynomial.

ax – by + y x z

Write the number of the term of the following polynomial.

23 + a x b ÷ 2

Separate monomials, binomials, trinomials and polynomials from the following algebraic expressions :

8 − 3x, xy², 3y² − 5y + 8, 9x − 3x² + 15x³ − 7,
3x × 5y, 3x ÷ 5y, 2y ÷ 7 + 3x − 7 and 4 − ax² + bx + y

Write the degree of a polynomial of the following:

xy + 7z

Write the degree of a polynomial of the following:

x² − 6x³ + 8

Write the degree of a polynomial of the following:

y − 6y² + 5y⁸

Write the degree of a polynomial of the following:

xyz − 3

Write the degree of a polynomial of the following:

xy + yz² − zx³

Write the degree of a polynomial of the following:

x⁵y⁷ – 8x³y⁸ + 10x⁴y⁴z⁴

Write the coefficient of :
ab in 7abx

Write the coefficient of :
7a in 7abx

Write the coefficient of :
5x² in 5x² – 5x

Write the coefficient of :
8 in a² – 8ax + a

Write the coefficient of :
4xy in x² – 4xy + y²

In `5/7`xy²z³, write the coefficient of 5

In `5/7`xy²z³, write the coefficient of `5/7`

In `5/7`xy²z³, write the coefficient of 5x

In `5/7`xy²z³, write the coefficient of xy²

In `5/7`xy²z³, write the coefficient of z³

In `5/7`xy²z³, write the coefficient of xz³

In `5/7`xy²z³, write the coefficient of 5xy²

In `5/7`xy²z³, write the coefficient of `1/7` yz

In `5/7`xy²z³, write the coefficient of z

In `5/7`xy²z³, write the coefficient of yz²

In `5/7` xy²z³, write the coefficient of 5xyz

In the polynomial, given below, separate the like terms :

3xy, − 4yx², 2xy², 2.5x²y, −8yx, −3.2y²x and x²y

In the polynomial, given below, separate the like terms :

y²z³, xy²z³, −5x²yz, −4y²z³, −8xz³y², 3x²yz and 2z³y²

Evaluate :

−7x² + 18x² + 3x² − 5x²

Evaluate :

b²y − 9b²y + 2b²y − 5b²y

Evaluate :

abx − 15abx − 10abx + 32abx

Evaluate :

7x − 9y + 3 − 3x − 5y + 8

Evaluate :

3x² + 5xy − 4y² + x² − 8xy − 5y²

Add : 5a + 3b, a − 2b, 3a + 5b

Add : 8x − 3y + 7z, −4x + 5y − 4z, −x − y − 2z

Add : 3b − 7c + 10, 5c −  2b −  15, 15 + 12c + b

Add : a − 3b + 3; 2a + 5 − 3c; 6c − 15 + 6b

Add : 13ab − 9cd − xy, 5xy, 15cd − 7ab, 6xy − 3cd

Add : x³ − x²y + 5xy² + y³, - x³ − 9xy² + y³, 3x²y + 9xy²

Find the total savings of a boy who saves ₹ (4x – 6y), ₹ (6x + 2y), ₹ (4y – x) and ₹ (y – 2x) for four consecutive weeks.

Subtract : 4xy² from 3xy²

Subtract : −2x²y + 3xy² from 8x²y

Subtract : 3a − 5b + c + 2d from 7a − 3b + c − 2d

Subtract : x³ − 4x − 1 from 3x³ − x² + 6

Subtract : 6a + 3 from a³ − 3a² + 4a + 1

Subtract : cab − 4cad − cbd from 3abc + 5bcd − cda

Subtract : a² + ab + b² from 4a² − 3ab + 2b²

Take away – 3x³ + 4x² – 5x+ 6 from 3x³ – 4x² + 5x – 6

Take m² + m + 4 from −m² + 3m + 6 and the result from m² + m + 1.

Subtract the sum of 5y² + y – 3 and y² – 3y + 7 from 6y² + y – 2.

What must be added to x⁴ – x³ + x² + x + 3 to obtain x⁴ + x² – 1 ?

How much more than 2x² + 4xy + 2y² is 5x² + 10xy – y² ?

How much less 2a² + 1 is than 3a² – 6 ?

If x = 6a + 8b + 9c ; y = 2b – 3a – 6c and z = c – b + 3a ; find :

1. x + y + z
2. x – y + z
3. 2x – y – 3z
4. 3y – 2z – 5x

The sides of a triangle are x² – 3xy + 8, 4x² + 5xy – 3 and 6 – 3x² + 4xy. Find its perimeter.

The perimeter of a triangle is 8y² – 9y + 4 and its two sides are 3y² – 5y and 4y² + 12. Find its third side.

The two adjacent sides of a rectangle are 2x² – 5xy + 3z² and 4xy – x² – z². Find its perimeter.

What must be subtracted from 19x⁴ + 2x³ + 30x – 37 to get 8x⁴ + 22x³ – 7x – 60 ?

How much smaller is 15x – 18y + 19z than 22x – 20y – 13z + 26 ?

How much bigger is 5x²y² – 18xy² – 10x²y than –5x² + 6x²y – 7xy?

Multiply : 8ab² by − 4a³b⁴

Multiply: `2/3"ab"` by `-1/4 "a"^2"b"`

Multiply: −5cd² by − 5cd²

Multiply: 4a and 6a + 7

Multiply: −8x and 4 − 2x − x²

Multiply: 2a² − 5a − 4 and −3a

Multiply: x + 4 by x − 5

Multiply: 5a − 1 by 7a − 3

Multiply: 12a + 5b by 7a − b

Multiply: x²+ x + 1 by 1 − x

Multiply: 2m² − 3m − 1 and 4m² − m − 1

Multiply: a², ab and b²

Multiply: abx, −3a²x and 7b²x³

Multiply: −3bx, −5xy and −7b³y²

Multiply: `-3/2"x"^5"y"^3` and `4/9"a"^2"x"3"y"`

Multiply: `-2/3"a"^7"b"^2` and `-9/4"a""b"^5`

Multiply: `2"a"^3-3"a"^2"b"` and `-1/2"ab"^2`

Multiply: `2"x"+1/2"y"` and `2"x"-1/2"y"`

Multiply: 5x² - 8xy + 6y² - 3by - 3xy

Multiply: `3-2/3 "xy"+5/7 "xy"^2-16/21 "x"^2"y"` by `− 21"x"^2"y"^2`

Multiply: 6x³ − 5x + 10 by 4 − 3x²

Multiply: 2y − 4y³ + 6y⁵ by y² + y − 3

Multiply: 5p² + 25pq + 4q² by 2p² − 2pq +3q²

Simplify : (7x – 8) (3x + 2)

Simplify : (px – q) (px + q)

Simplify: (5a + 5b – c) (2b – 3c)

Simplify :  (4x – 5y) (5x – 4y)

Simplify : (3y + 4z) (3y – 4z) + (2y + 7z) (y + z)

The adjacent sides of a rectangle are x² – 4xy + 7y² and x³ – 5xy². Find its area.

The base and the altitude of a triangle are (3x – 4y) and (6x + 5y) respectively. Find its area.

Multiply -4xy³ and 6x²y and verify your result for x = 2 and y= 1.

Find the value of (3x³) × (-5xy²) × (2x²yz³) for x = 1, y = 2 and z = 3.

Evaluate (3x⁴y²) (2x²y³) for x = 1 and y = 2.

Evaluate (x⁵) × (3x²) × (-2x) for x = 1.

If x = 2 and y = 1; find the value of (−4x²y³) × (−5x²y⁵).

Evaluate: (3x – 2)(x + 5) for x = 2.

Evaluate: (2x – 5y)(2x + 3y) for x = 2 and y = 3.

Evaluate: xz (x² + y²) for x = 2, y = 1 and z= 1.

Evaluate: x(x – 5) + 2 for x = 1.

Evaluate: xy²(x – 5y) + 1 for x = 2 and y = 1.

Evaluate: 2x(3x – 5) – 5(x – 2) – 18 for x = 2.

Multiply and then verify :
−3x²y² and (x – 2y) for x = 1 and y = 2.

Multiply: 2x² – 4x + 5 by x² + 3x – 7

Multiply:  (ab – 1) (3 – 2ab)

Simplify : (5 – x) (6 – 5x) (2 -x).

Divide: −70a³ by 14a²

Divide: 24x³y³ by −8y²

Divide: 15a⁴b by −5a³b

Divide: −24x⁴d³ by −2x²d⁵

Divide: 63a⁴b⁵c⁶ by −9a²b⁴c³

Divide: 8x − 10y + 6c by 2

Divide: 15a³b⁴ − 10a⁴b³ − 25a³b⁶ by −5a³b²

Divide: −14x⁶y³ − 21x⁴y⁵ + 7x⁵y⁴ by 7x²y²

Divide: a² + 7a + 12 by a + 4

Divide: x² + 3x − 54 by x − 6

Divide: 12x² + 7xy − 12y² by 3x + 4y

Divide: x⁶ − 8 by x² − 2

Divide: 6x³ − 13x² − 13x + 30 by 2x² − x − 6

Divide: 4a² + 12ab + 9b² − 25c² by 2a + 3b + 5c

Divide: 16 + 8x + x⁶ − 8x³ − 2x⁴ + x² by x + 4 − x³

Find the quotient and the remainder when :
a³ − 5a² + 8a + 15 is divided by a + 1. verify your answer.

Find the quotient and the remainder when :
3x⁴ + 6x³ − 6x² + 2x − 7 is divided by x − 3. verify your answer.

Find the quotient and the remainder when :
6x² + x  − 15 is divided by 3x + 5. verify your answer.

The area of a rectangle is x³ – 8x + 7 and one of its sides is x – 1. Find the length of the adjacent side.

The product of two numbers-is 16x⁴ – 1. If one number is 2x – 1, find the other.

Divide x⁶ – y⁶ by the product of x² + xy + y² and x – y.

Simplify : a² − 2a + {5a² − (3a - 4a²)}

Simplify : `"x" − "y" − {"x" − "y" − ("x" + "y") −overline("x"-"y")}`

Simplify : −3 (1 − x²) − 2{x² − (3 − 2x²)}

Simplify : `2{m-3(n+overline(m-2n))}`

Simplify : `3"x"-[3"x"-{3"x"-(3"x"-overline(3"x"-"y"))}]`

Simplify : `"p"^2"x"-2{"px"-3"x"("x"^2-overline(3"a"-"x"^2))}`

Simplify : `2[6 + 4 {"m"-6(7 - overline("n"+"p")) + "q"}]`

Simplify : `"a"-["a"-overline("b+a") - {"a"-("a"- overline("b"-"a"))}]`

Simplify : `3"x"-[4"x"-overline(3"x"-5"y")-3  {2"x"-(3"x"-overline(2"x"-3"y"))}]`

Simplify: a⁵ ÷ a³ + 3a × 2a

Simplify: x⁵ ÷ (x² × y²) × y³

Simplify: (x⁵ ÷ x²) × y² × y³

Simplify: (y³ − 5y²) ÷ y × (y − 1)

Simplify: `3"a"xx[8"b" ÷ 4-6{"a"-(5"a"-overline(3"b"-2"a"))} ]`

Simplify: 7x + 4 {x² ÷ (5x ÷ 10)} − 3 {2 − x³ ÷ (3x² ÷ x)}