## 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:

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 situation.

Solution:

Question 3.

Write down the algebraic expression whose terms are:

(i) 5a, -3b, c

(ii) x^{2}, -5x, 6

(iii) x^{2}y, xy, -xy^{2}

Solution:

Question 4.

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

(i) 3 – 7x

(ii) 2 – 5a + \(\frac { 1 }{ 2 }\) b

(iii) 3x^{5} + 4y^{3} – 7xy^{2} + 3

Solution:

Question 5.

Identify the terms and their factors in the algebraic expressions given below:

(i) -4x + 5y

(ii) xy + 2x^{2}y^{2}

(iii) 1.2ab – 2.4b + 3.6a

Solution:

Question 6.

Show the terms and their factors by tree diagrams of the following algebraic expressions:

(i) 8x + 3y^{2}

(ii) y – y^{3}

(iii) 5xy^{2} + 7x^{2}y

(iv) -ab + 2b^{2} – 3a^{2}

Solution:

Question 7.

Write down the numerical coefficient of each of the following:

(i) -7x

(ii) -2x^{3}y^{2}

(iii) 6abcd^{2}

(iv) \(\frac { 2 }{ 3 }\) pq^{2}

Solution:

Question 8.

Write down the coefficient of x in the following:

(i) -4bx

(ii) 5xyz

(iii) -x

(iv) -3x^{2}y

Solution:

Question 9.

In -7xy^{2}z^{3}, write down the coefficient of:

(i) 7x

(ii) -xy^{2}

(iii) xyz

(iv) 7yz^{2}

Solution:

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 – 3x^{2}

(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) 13y^{2} – 8xy

(ii) 7x – xy^{2}

(iii) 5 – 7xyz + 4x^{2}y

Solution:

Question 12.

Identify the term which contain y2 and write the coefficient of y2 in each of the following expressions:

(i) 8 – xy^{2}

(ii) 5y^{2} + 7x – 3xy^{2}

(iii) 2x^{2}y – 15xy^{2} + 7y^{2}

Solution:

Question 13.

Classify into monomials, binomials and trinomials:

(i) 4y – 7z

(ii) -5xy^{2}

(iii) x + y – xy

(iv) ab^{2} – 5b -3a

(v) 4p^{2}q – 5pq^{2}

(vi) 2017

(vii) 1 + x + x^{2}

(viii) 5x^{2} – 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) 4m^{2}p, 4mp^{2}

(v) 12xz, 12x^{2}z^{2}

(vi) -5pq, 7qp

Solution:

Question 15.

Identify like terms in the following:

(i) x^{2}y, 3xy^{2}, -2x^{2}y, 4x^{2}y^{2}

(ii) 3a^{2}b, 2abc, -6a^{2}b, 4abc

(iii) 10pq, 7p, 8q – p^{2}q^{2}, -7qp, -100q, -23, 12q^{2}p^{2}, -5p^{2}, 41, 2405p, 78qp, 13p^{2}q, qp^{2}, 701p^{2}

Solution:

Question 16.

Write down the degree of following polynomials in x:

(i) x^{2} – 6x^{7} + x^{8}

(ii) 3 – 2x

(iii) -2

(iv) 1 – x^{2}

Solution:

Question 17.

Write the degree of the following polynomials:

(i) 3x^{2} – 5xy^{2} + 7

(ii) xy^{2} – y^{3} + 3y^{4} – 2

(iii) 7 – 2x^{3} – 5xy^{3} + 9y^{5}

Solution:

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) 7x^{3} + 2x^{2} + 3x – 5 is a polynomial

(vi) 2x^{2} – \(\frac { 3 }{ x }\) is a polynomial

(vii) Coefficient of x in -3xy is -3

Solution: