R d sharma solutions mathematics class 7 Solutions for Chapter 7 algebraic expressions

Exercises in Chapter 7 algebraic expressions Grade 7

Algebraic Expressions Exercise 7.1

Algebraic Expressions Exercise 7.2

Algebraic Expressions Exercise 7.3

Algebraic Expressions Exercise 7.4

Questions in Algebraic Expressions Exercise 7.1

Identify the monomials, binomials, trinomialsand quadrinomials from the following expressions:

(i) a2

(ii) a2 − b2

(iii) x3 + y3+ z3

(iv) x3 + y3+z3 + 3xyz

(v) 7 + 5

(vi) a b c + 1

(vii) 3x – 2 + 5

(viii) 2x – 3y + 4

(ix) x y + y z + z x

(x) ax3 +bx2 + cx + d

Write all the terms of each of the following algebraic expressions:

(i) 3x

(ii) 2x – 3

(iii) 2x2 − 7

(iv)2x2 + y2− 3xy +4

Identify the terms and also mention the numerical coefficients of those terms:

(i) 4xy, -5x2y, -3yx, 2xy2

(ii) 7a2bc,-3ca2b, -(5/2)abc2, 3/2abc2, (-4/3)cba2

Identify the like terms in the following algebraic expressions:

(i) a2 + b2 -2a2 + c2 + 4a

(ii) 3x + 4xy − 2yz + 52zy

(iii) abc + ab2c+ 2acb2 + 3c2ab + b2ac − 2a2bc + 3cab2

Write the coefficient of x in thefollowing:

(i) –12x

(ii) –7xy

(iii) xyz

(iv) –7ax

Three numbers are in the ratio 2: 3: 5 and the sum of these numbers is 800. Find the numbers

Write the coefficient of x2 in the following:

(i) −3x2

(ii) 5x2yz

(iii) 5/7x2z

(iv) (-3/2) ax2 + yx

Write the coefficient of:

(i) y in –3y

(ii) a in 2ab

(iii) z in –7xyz

(iv) p in –3pqr

(v) y2 in 9xy2z

(vi) x3 in x3 +1

(vii) x2 in −x2

Write the numerical coefficient of each in the following:

(i) xy

(ii) -6yz

(iii) 7abc

(iv) -2x3y2z

Write the numericalcoefficient of each term in the followingalgebraic expressions:

(i)4x2y – (3/2)xy + 5/2 xy2

(ii) (–5/3)x2y+ (7/4)xyz + 3

Write the constant term of each of the following algebraic expressions:

(i) x2y− xy2 + 7xy − 3

(ii) a3− 3a2 + 7a + 5

Evaluate each of the following algebraic expressions for x = 1, y = -1, z = 2, a = -2, b = 1, c = -2:

(i) ax + by + cz

(ii) ax2 +by2 – cz

(iii) axy + byz + cxy

Questions in Algebraic Expressions Exercise 7.2

Add the following:

(i) 3x and 7x

(ii)-5xy and 9xy

Simplify the following algebraic expressions by removing grouping symbols.

2x + (5x – 3y)

Simplify each of the following:

(i) 7x3y +9yx3

(ii) 12a2b+ 3ba2

Add the following:

(i) 7abc, -5abc,9abc, -8abc

(ii) 2x2y,- 4x2y, 6x2y, -5x2y

Add the following expressions:

(i) x3 -2x2y+ 3xy2- y3, 2x3- 5xy2 + 3x2y- 4y3

(ii) a4 - 2a3b+ 3ab3 + 4a2b2 + 3b4, - 2a4- 5ab3 + 7a3b - 6a2b2 + b4

Add the following expressions:

(i) 8a – 6ab +5b, –6a – ab – 8b and –4a + 2ab + 3b

(ii) 5x3+ 7 + 6x - 5x2, 2x2 – 8 - 9x, 4x - 2x2 + 3 x 3, 3 x 3 - 9x - x2 and x - x2 - x3 – 4

Add the following:

(i) x – 3y – 2z

5x + 7y – 8z

3x – 2y + 5z

(ii) 4ab – 5bc + 7ca

–3ab + 2bc – 3ca

5ab – 3bc + 4ca

Add 2x2 - 3x + 1 to the sum of 3x2 - 2x and 3x+ 7.

Add x2 + 2xy + y2 to the sum of x2 - 3y2and 2x2 - y2 + 9.

Add a3+ b3 - 3 to the sum of 2a3 -3b3 - 3ab + 7 and -a3 + b3 + 3ab - 9.

Subtract:

(i) 7a2b from 3a2b

(ii) 4xy from -3xy

Subtract:

(i) - 4x from 3y

(ii) - 2x from – 5y

Subtract:

(i) 6x3 −7x2+ 5x − 3 from 4 − 5x + 6x2 − 8x3

(ii) − x2−3z from 5x2– y + z + 7

(iii) x3 +2x2y + 6xy2 − y3 from y3−3xy2−4x2y

From

(i) p3 – 4+ 3p2, take away 5p2 − 3p3 + p − 6

(ii) 7 + x − x2,take away 9 + x + 3x2 + 7x3

(iii) 1− 5y2,take away y3 + 7y2 + y +1

(iv) x3 −5x2 + 3x + 1, take away 6x2 − 4x3 + 5 + 3x

From the sum of 3x2 − 5x + 2 and − 5x2 − 8x +9 subtract 4x2 − 7x + 9.

Subtract the sum of13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7.

From the sum of x2 + 3y2 − 6xy, 2x2 − y2 + 8xy, y2 + 8 and x2 − 3xy subtract−3x2 + 4y2– xy + x – y + 3.

What should be added to xy –3yz + 4zx to get 4xy – 3zx + 4yz + 7?

What should be subtracted from x2 – xy + y2 – x + y + 3 to obtain −x2 + 3y2 − 4xy + 1?

How much is x – 2y + 3z greater than 3x + 5y – 7?

How much is x2 − 2xy + 3y2 less than 2x2− 3y2 + xy?

How much does a2 − 3ab + 2b2 exceed 2a2 − 7ab + 9b2?

What must be added to 12x3 − 4x2 + 3x − 7 to make the sum x3 + 2x2 − 3x + 2?

If P = 7x2 + 5xy − 9y2, Q = 4y2 − 3x2 − 6xy and R = −4x2 + xy + 5y2, show that P + Q + R = 0.

If P = a2 − b2 + 2ab, Q = a2 + 4b2 −6ab, R = b2 + b, S = a2 − 4ab and T = −2a2 + b2– ab + a.

Find P + Q + R + S – T.

Questions in Algebraic Expressions Exercise 7.3

Place the last two terms ofthe following expressions in parentheses precededbya minus sign:

(i) x + y – 3z + y

(ii) 3x – 2y – 5z – 4

(iii) 3a – 2b + 4c – 5

(iv) 7a + 3b + 2c + 4 (v) 2a2 - b2 - 3ab+ 6

(vi)a2 + b2 - c2 + ab - 3ac

Write each of the following statements by using appropriate grouping symbols:

(i) The sum of a – b and 3a – 2b + 5 is subtracted from 4a + 2b – 7.

(ii) Three times the sum of 2x + y – [5 – (x – 3y)] and 7x – 4y + 3 is subtracted from 3x – 4y + 7

(iii) The subtraction of x2 - y2 + 4xyfrom 2x2 + y2 - 3xy is added to 9x2 - 3y2- xy.

Questions in Algebraic Expressions Exercise 7.4

Simplify the following algebraic expressions by removing grouping symbols.

5a – (3b – 2a + 4c)

Simplify the following algebraic expressions by removing grouping symbols.

5a – (3b – 2a + 4c)

Simplify the following algebraic expressions by removing grouping symbols.

-2(x2 - y2+ xy) - 3(x2 +y2 - xy)

Simplify the following algebraic expressions by removing grouping symbols.

3x + 2y – {x – (2y – 3)}

Simplify the following algebraic expressions by removing grouping symbols.

5a – {3a – (2 – a) + 4}

Simplify the following algebraic expressions by removing grouping symbols.

a – [b – {a – (b – 1) + 3a}]

Simplify the following algebraic expressions by removing grouping symbols.

a – [2b – {3a – (2b – 3c)}]

Simplify the following algebraic expressions by removing grouping symbols.

-x + [5y – {2x – (3y –5x)}]

Simplify the following algebraic expressions by removing grouping symbols.

2a – [4b – {4a – 3(2a –b)}]

Simplify the following algebraic expressions by removing grouping symbols.

-a – [a + {a + b – 2a – (a– 2b)} - b]

Simplify the following algebraic expressions by removing grouping symbols.

2x – 3y – [3x – 2y -{x – z– (x – 2y)}]

Simplify the following algebraic expressions by removing grouping symbols.

5 + [x – {2y – (6x + y – 4)+ 2x} – {x – (y – 2)}]

Simplify the following algebraic expressions by removing grouping symbols.

x2 - [3x + [2x -(x2 - 1)] + 2]

Simplify the following algebraic expressions by removing grouping symbols.

20 - [5xy + 3[x2- (xy - y) - (x - y)]]

Simplify the following algebraic expressions by removing grouping symbols.

85 – [12x – 7(8x – 3) –2{10x – 5(2 – 4x)}]

Simplify the following algebraic expressions by removing grouping symbols.

xy [yz – zx – {yx – (3y –xz) – (xy – zy)}]

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Chapters in this book

Integers

Fractions

Decimals

Rational Numbers

Operations on Rational Numbers

Exponents

Algebraic Expressions

Linear Equations In One Variable

Ratio and Proportion

Unitary Method

Percentage

Profit and Loss

Simple Interest

Lines and Angles

Properties of Triangle

Congruence

Constructions

Symmetry

Visualising Solid Shapes

Mensuration 1

Mensuration 2 Area of Circle

Data Handling-Collection Organisation Data

Data Handling-Central Values

Data Handling-Construction Of Bar Graphs

Data Handling-Probability