R s aggarwal solutions mathematics class 8 Solutions for Chapter 6 operations on algebraic expressions

Exercises in Chapter 6 operations on algebraic expressions Grade 8

Operations on Algebraic Expressions Exercise 6A

Operations on Algebraic Expressions Exercise 6B

Operations on Algebraic Expressions Exercise 6C

Operations on Algebraic Expressions Exercise 6D

Operations on Algebraic Expressions Exercise 6E

Questions in Operations on Algebraic Expressions Exercise 6A

Add: 8ab, -5ab, 3ab, -ab

Add: 7x, -3x, 5x, -x, -3x

Add: 3a-3b+4c, 2a+3b-8c, a-6b+c

Add: 6ax-2by+3cz, 6by-11ax-cz and 10cz-2ax-3by

Add: $2x^3-9x^2+8,3x^2-6x-5,7x^3-10x+1\text{ and }3+2x-5x^2-4x^3$

Add: 6p+4q-r+3, 2r-5p-6, 11q-7p+2r-1 and 2q-3r+4

Add: $4x^2-7xy+4y^2-3,5+6y^2-8xy+x^2\text{ and }6-2xy+2x^2-5y^2$

Subtract: $3a^2b\text{ from }-5a^2b$

Subtract: -8pq from 6pq

Subtract: -2abc from -8abc

Subtract: -16p from -11p

Subtract: 2a-5b+2c-9 from 3a-4b-c+6

Find each of the following products:

$\left(x^2+xy+y^2\right)\times(x-y)$

Questions in Operations on Algebraic Expressions Exercise 6B

Find each of the following products:

(5x + 7) × (3x + 4)

Find each of the following products: (4x + 9) × (x – 6)

Find each of the following products:

(2x +5 ) × (4x – 3)

Find each of the following products:

(3y – 8) × (5y – 1)

Find each of the following products:

(7x + 2y) × (x + 4y)

Find each of the following products: (9x + 5y) × (4x + 3y)

Find each of the following products: (3m – 4n) × (2m – 3n)

Find each of the following products: $\left(x^2-a^2\right)\times(x-a)$

Find each of the following products: $\left(x^2-y^2\right)\times(x+2y)$

Find each of the following products: $\left(3p^2+q^2\right)\times\left(x^2-y^2\right)$

Find each of the following products: $\left(2x^2-5y^2\right)\times\left(x^2+3y^2\right)$

Find each of the following products: $\left(x^3-y^3\right)\times\left(x^2+y^2\right)$

Find each of the following products: $\left(x^4+y^4\right)\times\left(x^2-y^2\right)$

Find each of the following products: $\left(x^{4}+\left(1 / x^{4}\right) \times(x+(1 / x))\right.$

Find each of the following products: $\left(x^2-3x+7\right)\times(2x+3)$

Find each of the following products: $\left(3x^2+5x-9\right)\times(3x-5)$

Find each of the following products:

$\left(x^2-xy+y^2\right)\times(x+y)$

Questions in Operations on Algebraic Expressions Exercise 6C

Divide: $24x^2y^3\text{ by }3xy$

Divide: $36xyz^2\text{ by }-9xz$

Divide: $-72x^2y^2z\text{ by }-12xyz$

Divide: $-56mnp^2\text{ by }7mnp$

Divide: $5m^2-30m^2+45m\text{ by }5m$

Divide: $8x^2y^2-6xy^2+10x^2y^2\text{ by }2xy$

Divide: $9x^2y-6xy+12xy^2by-3xy$

Divide: $12x^2+8x^3-6x^2\text{ by }-2x^2$

Write the quotient and remainder when we divide:

$\left(x^2-4x+4\right)\text{ by }(x-2)$

Write the quotient and remainder when we divide:

$\left(x^2-4\right)\text{ by }(x+2)$

Write the quotient and remainder when we divide:

$\left(x^2+12x+35\right)\text{ by }(x+7)$

Write the quotient and remainder when we divide: $\left(15x^2+x-6\right)\text{ by }(3x+2)$

Write the quotient and remainder when we divide:

$\left(14x^2-53x+45\right)\text{ by }(7x-9)$

Expand: $\left((x / y)-((y / x))^{2}\right.$

Questions in Operations on Algebraic Expressions Exercise 6D

Find each of the following products:

(x + 6) (x +6)

Find each of the following products:

(4x +5y) (4x + 5y)

Find each of the following products:

(7a +9b) (7a +9b)

Find each of the following products:

((2/3) x + (4/5) y) ((2/3) x + (4/5) y)

Find each of the following products:

$\left(x^2+7\right)\left(x^2+7\right)$

Find each of the following products: $\left((5/6)\mathrm{a}^2+2\right)\left((5/6)\mathrm{a}^2+2\right)$

Find each of the following products:

(x – 4) (x – 4)

Find each of the following products:

(2x-3y) (2x-3y)

Find each of the following products:

((3/4) x – (5/6) y) ((3/4) x + (5/6) y)

Find each of the following products:

(x – (3/x) ) ( x – (3/x) )

Find each of the following products: $\left((1/3)x^2-9\right)\left((1/3)x^2-9\right)$

Find each of the following products:

$\left((1/2)\mathrm{y}^2-(1/3)\mathrm{y}\right)\left((1/2)\mathrm{y}^2-(1/3)\mathrm{y}\right)$

Expand: $(8a+3b)^2$

Expand: $(7x+2y)^2$

Expand: $(5x+11)^2$

Expand: $((a/2)+(2/a))^2$

Expand: $((3x/4)+(2y/9))^2$

Expand: $(9x-10)^2$

Expand: $\left(x^2y-yz^2\right)^{-2}$

Find each of the following products: (x+3) (x-3)

Find each of the following products: (2x+5) (2x-5)

Find each of the following products: (8+x) (8-x)

Find each of the following products: (7x+11y) (7x-11y)

Find each of the following products: $\left(5x^2+(3/4)y^2\right)\left(5x^2-(3/4)y^2\right)$

Find each of the following products:

((4x/5)-(5y/3)) ((4x/5) + (5y/3))

Find each of the following products: ((x + (1/x)) ((x-(1/x))

Find each of the following products: ((1/x) + (1/y)) ((1/x)-(1/y))

Find each of the following products: (2a + (3/b)) (2a – (3/b))

Using the formula for squaring a binomial, evaluate the following:

$(54)^2$

Using the formula for squaring a binomial, evaluate the following:

$(82)^2$

Using the formula for squaring a binomial, evaluate the following:

$(704)^2$

using the formula for squaring a binomial, evaluate the following:

$(69)^2$

using the formula for squaring a binomial, evaluate the following:

$(78)^2$

using the formula for squaring a binomial, evaluate the following:

$(197)^2$

using the formula for squaring a binomial, evaluate the following: $(999)^{2}$

Questions in Operations on Algebraic Expressions Exercise 6E

Select the correct answer in each of the following: The sum of (6a+4b-c+3), (2b-3c+4), (11b-7a+2c-1) and (2c-5a-6) is

(a) (4a-6b+2)

(b) (-3a+14b-3c+2)

(d) (-6a+6b+c-4)

Select the correct answer in each of the following:

$\left(3q+7p^2-2r^3+4\right)-\left(4p^2-2q+7r^3-3\right)=?$

$(a)\left(p^{2}+2 q+5 r^{3}+1\right)$

$\text { (b) }\left(11 p^{2}+q+5 r^{3}+1\right)$

$(c)\left(-3 p^{2}-5 q+9 r^{3}-7\right)$

$(d)\left(3 p^{2}+5 q-9 r^{3}+7\right)$

(x+5) (x-3) =? $\text { (a) } x^{2}+5 x-15$

$\text { (b) } x^{2}-3 x-15$

$\text { (c) } x^{2}+2 x+15$

$\text { (d) } x^{2}+2 x-15$

(2x+3) (3x-1) =?

$(a)\left(6x^2+8x-3\right)$

$(b)\left(6x^2+7x-3\right)$

$(c)\left(6x^2-7x-3\right)$

$(d)\left(6x^2-7x+3\right)$

(x+4) (x+4) =?

$\text{ (a) }\left(x^2+16\right)$

$\text{ (b) }\left(x^2+4x+16\right)$

$\text{ (c) }\left(x^2+8x+16\right)$

$\text{ (d) }\left(x^2+16x\right)$

(x-6) (x-6) =?

** ** $\text{ (a) }\left(x^2-36\right)$

$\text{ (b) }\left(x^2+36\right)$

$\text{ (c) }\left(x^2-6x+36\right)$

$(d)\left(x^2-12x+36\right)$

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Chapters in this book

Rational Numbers

Exponents

Squares and Square Roots

Cubes and Cube Roots

Playing with Numbers

Operations on Algebraic Expressions

Factorisation

Linear Equations

Percentage

Profit and Loss

Compound Interest

Direct and Inverse Proportions

Time and Work

Polygons

Parallelograms

Construction of Quadrilaterals

Area of a Trapezium and a Polygon

Three-Dimensional Figures

Volume and Surface Area of Solids

Data Handling

Introduction to Coordinate Geometry

Line Graphs and Linear Graphs

Pie Charts

Probability