ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Ex 8.1

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Ex 8.1

Question 1.
From the algebraic expressions using variables, constants, and arithmetic operations:
(i) 6 more than thrice a number x.
(ii) 5 times x is subtracted from 13.
(iii) The numbers x and y both squared and added.
(iv) Number 7 is added to 3 times the product of p and q.
(v) Three times of x is subtracted from the product of x with itself.
(vi) Sum of the numbers m and n is subtracted from their product.
Solution:
(i) 6 more than thrice a number x = 3x + 6
(ii) 5 times x is subtracted from 13 = 13 – 5x
(iii) The numbers x and y both squared and added = x² + y²
(iv) Number 7 is added to 3 times the product of p and q = 3pq + 1
(v) Three times of x is subtracted from the product of x with itself = x² – 3x
(vi) Sum of the numbers m and n is subtracted from their product = mn – (m + n)

Question 2.
A taxi charges ₹ 9 per km and a fixed charge of ₹ 50. If the taxi is hired for x km, write an algebraic expression for this situtation.
Solution:
Charges of a taxi = ₹ 9 per km
Fixed charges = ₹ 50
and taxi is hired for x km = (9x + 50) rupees

Question 3.
Write down the algebraic expression whose terms are:
(i) 5a, -3b, c
(ii) x², -5x, 6
(iii) x²y, xy, -xy²
Solution:
(i) 5a – 3b + c
(ii) x² – 5x + 6
(iii) x²y + xy – xy²

Question 4.
Write all the terms of each of the following algebraic expressions:
(i) 3 – 7x
(ii) 2 – 5a + \(\frac { 1 }{ 2 }\) b
(iii) 3x⁵ + 4y³ – 7xy² + 3
Solution:
(i) 3 – 7x = 3, -7x
(ii) 2 – 5a + \(\frac { 3 }{ 2 }\) b = 2, -5a, \(\frac { 3 }{ 2 }\) b
(iii) 3x⁵ + 4y³ – 7xy² + 3 = 3x⁵, 4y³, -7xy², 3

Question 5.
Identify the terms and their factors in the algebraic expressions given below:
(i) -4x + 5y
(ii) xy + 2x²y²
(iii) 1.2ab – 2.4b + 3.6a
Solution:
(i) -4x + 5y
-4x = -4, x
5y = 5, y
(ii) xy + 2x²y²
xy = x, y
2x²y² = 2, x, x, y, y
(iii) 1.2ab – 2.4b + 3.6a
1.2ab = 1.2, a, b
-2.4b = -2.4, b
3.6a = 3.6, a

Question 6.
Show the terms and their factors by tree diagrams of the following algebraic expressions:
(i) 8x + 3y²
(ii) y – y³
(iii) 5xy² + 7x²y
(iv) -ab + 2b² – 3a²
Solution:
(i) 8x + 3y²

Question 7.
Write down the numerical coefficient of each of the following:
(i) -7x
(ii) -2x³y²
(iii) 6abcd²
(iv) \(\frac { 2 }{ 3 }\) pq²
Solution:
Numerical co-efficient
(i) -7x – numerical co-efficient is -7
(ii) -2x³y² – numerical co-efficient is -2
(iii) 6abcd² – numerical co-efficient is 6
(iv) \(\frac { 2 }{ 3 }\) pq² – numerical co-efficient is \(\frac { 2 }{ 3 }\)

Question 8.
Write down the coefficient of x in the following:
(i) -4bx
(ii) 5xyz
(iii) -x
(iv) -3x²y
Solution:
coefficient of x
(i) -4bx – -4b
(ii) 5xyz – 5yz
(iii) -x – -1
(iv) -3x²y – -3xy

Question 9.
In -7xy²z³, write down the coefficient of:
(i) 7x
(ii) -xy²
(iii) xyz
(iv) 7yz²
Solution:
In -7xy²z³
(i) Co-efficient of 7x = -y²z³
(ii) Co-efficient of -xy² = 7z³
(iii) Co-efficient of xyz = -7yz²
(iv) Co-efficient of 7yz² = -xyz

Question 10.
Identify the terms (other than constants) and write their numerical coefficients in each of the following algebraic expressions:
(i) 3 – 7x
(ii) 1 + 2x – 3x²
(iii) 1.2a + 0.8b
Solution:

Question 11.
Identify the terms which contain x and write the coefficient of x in each of the following expressions:
(i) 13y² – 8xy
(ii) 7x – xy²
(iii) 5 – 7xyz + 4x²y
Solution:

Question 12.
Identify the term which contain y2 and write the coefficient of y2 in each of the following expressions:
(i) 8 – xy²
(ii) 5y² + 7x – 3xy²
(iii) 2x²y – 15xy² + 7y²
Solution:

Question 13.
Classify into monomials, binomials and trinomials:
(i) 4y – 7z
(ii) -5xy²
(iii) x + y – xy
(iv) ab² – 5b -3a
(v) 4p²q – 5pq²
(vi) 2017
(vii) 1 + x + x²
(viii) 5x² – 7 + 3x + 4
Solution:

Question 14.
State whether the given pair of terms is of like or unlike terms:
(i) -7x, \(\frac { 5 }{ 2 }\) x
(ii) -29x, -29y
(iii) 2xy, 2xyz
(iv) 4m²p, 4mp²
(v) 12xz, 12x²z²
(vi) -5pq, 7qp
Solution:
(i) -7x, \(\frac { 5 }{ 2 }\) x – Like
(ii) -29x, -29y – Unlike
(iii) 2xy, 2xyz – Unlike
(iv) 4m²p, 4mp² – Unlike
(v) 12xz, 12x²z² – Unlike
(vi) -5pq, 7qp – Like

Question 15.
Identify like terms in the following:
(i) x²y, 3xy², -2x²y, 4x²y²
(ii) 3a²b, 2abc, -6a²b, 4abc
(iii) 10pq, 7p, 8q – p²q², -7qp, -100q, -23, 12q²p², -5p², 41, 2405p, 78qp, 13p²q, qp², 701p²
Solution:
(i) x²y and -2x²y are like terms.
(ii) 3a²b, -6a²b and 2abc, 4abc are pairs of like terms.
(iii) 10pq, -7qp, 78qp and 7p, 2405p and 8q, -100q,
and -p²q², 12q²p² and -23, 41 and -5p², 701p²
and 13p²q, qp² are groups of like terms.

Question 16.
Write down the degree of following polynomials in x:
(i) x² – 6x⁷ + x⁸
(ii) 3 – 2x
(iii) -2
(iv) 1 – x²
Solution:
(i) x² – 6x⁷ + x⁸ ; degree is 8
(ii) 3 – 2x; degree is 1
(iii) -2 ; degree is 0
(iv) 1 – x² ; degree is 2

Question 17.
Write the degree of the following polynomials:
(i) 3x² – 5xy² + 7
(ii) xy² – y³ + 3y⁴ – 2
(iii) 7 – 2x³ – 5xy³ + 9y⁵
Solution:
(i) 3x² – 5xy² + 1 ; degree is 1 + 2 = 3
(ii) xy² – y³ + 3y⁴ – 2 ; degree is 4
(iii) 7 – 2x³ – 5xy³ + 9y⁵ ; degree is 5

Question 18.
State true or false:
(i) If 5 is constant andy is variable, then 5y and 5 + y are variables
(ii) 7x has two terms, 7 and x
(iii) 5 + xy is a trinomial
(iv) 7a × bc is a binomial
(v) 7x³ + 2x² + 3x – 5 is a polynomial
(vi) 2x² – \(\frac { 3 }{ x }\) is a polynomial
(vii) Coefficient of x in -3xy is -3
Solution:
(i) True.
(ii) False. Correct: 7x has one term.
(iii) False. Correct: It is bionomial.
(iv) False. Correct: It is 7abc monomial.
(v) True.
(vi) False. Correct: It is bionomial.
(vii) False. Correct: It is -3y.

ML Aggarwal Class 7 Solutions for ICSE Maths