## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Check Your Progress

Question 1.

Consider the expression \(\frac { 3 }{ 2 }\) x^{2}y – \(\frac { 1 }{ 2 }\) xy^{2} + 6x^{2}y^{2}.

(i) How many terms are there? What do you call such an expression?

(ii) List out the terms.

(iii) In the term \(\frac { -1 }{ 2 }\) xy^{2}, write down the numerical coefficient and the literal coefficient.

(iv) In the term \(\frac { -1 }{ 2 }\) xy^{2}, what is the coefficient of x?

Solution:

\(\frac { 3 }{ 2 }\) x^{2}y – \(\frac { 1 }{ 2 }\) xy^{2} + 6x^{2}y^{2}

(i) It has 3 terms : Trinomial

(ii) \(\frac { 3 }{ 2 }\) x^{2}y, \(\frac { -1 }{ 2 }\) xy^{2}, 6x^{2}y^{2}

(iii) In \(\frac { -1 }{ 2 }\) xy^{2},

numerical coefficient = \(\frac { -1 }{ 2 }\)

Literal coefficient = xy^{2}

(iv) In the term \(\frac { -1 }{ 2 }\) xy^{2}

coefficient of x = \(\frac { -1 }{ 2 }\) y^{2}

Question 2.

Write the Degree of the following polynomials:

(i) \(\frac { 2 }{ 5 }\) x^{3} – 7x^{2} – \(\frac { 1 }{ 2 }\) x + 3

(ii) \(\frac { 2 }{ 3 }\) xy^{2} – 5xy + \(\frac { 3 }{ 5 }\) y^{2}x^{2} + 2x

Solution:

Question 3.

Identify monomials, binomials and trinomials from the following algebraic expressions:

(i) 5x × y

(ii) 3 – 5x

(iii) \(\frac { 1 }{ 2 }\) (7x – 3y + 5z)

(iv) 3x^{2} – 1.2xy

(v) -3x^{3}y^{4}z^{5}

(vi) 5x(2x – 3y) + 7x^{2}

Solution:

Question 4.

Using horizontal method:

(i) Add x^{2} + y^{2} – 2xy, -2x^{2} – y^{2} – 2xy and 3x^{2} + y^{2} + xy

(ii) Subtract -x^{2} + y^{2} + 2xy from 2x^{2} – 3y^{2}.

Solution:

(i) x^{2} + y^{2} – 2xy – 2x^{2} – y^{2} – 2xy + 3x^{2} + y^{2} + xy

= x^{2} – 2x^{2} + 3x^{2} + y^{2} – y^{2} + y^{2} – 2xy – 2xy + xy

= 2x^{2} + y^{2} – 3xy

(ii) (2x^{2} – 3y^{2}) – (-x^{2} + y^{2} + 2xy)

= 2x^{2} – 3y^{2} + x^{2} – y^{2} – 2xy

= 3x^{2} – 4y^{2} – 2xy

Question 5.

Using column method, add ab + 2bc – ca and 2ab – bc – ca and subtract 4ab + 5bc – 3ca.

Solution:

Question 6.

The sides fo a triangle are 5a – 3b, 3a + 2b and 5b – 2a, find its perimeter.

Solution:

Sides of a triangle are 5a – 3b, 3a + 2b and 5b – 2a

Perimeter = 5a – 3b + 3a + 2b + 5b – 2a

= 8a – 2a + 4b

= 6a + 4b

Question 7.

If two adjacent sides of a rectangle are 4x +7y and 3y – x, find its perimeter.

Solution:

Two adjacent sides of a rectangle are 4x + 7y and 3y – x

Perimeter = 2(4x + 7y + 3y – x) = 2(3x + 10y) = 6x + 20y

Question 8.

Subtract the sum of 3x^{2} + 2xy – 2y^{2} and 5y^{2} – 7xy from 5x^{2} + 2y^{2} – 3xy.

Solution:

Sum of 3x^{2} + 2xy – 2y^{2} and 5y^{2} – 7xy

= 3x^{2} + 2xy – 2y^{2} + 5y^{2} – 7xy

= 3x^{2} – 5xy + 3y^{2}

Now,

Question 9.

What must be added to 5x^{3} – 2x^{2} + 3x + 7 to get 7x^{3} + 7x – 5?

Solution:

Required expression

= 7x^{3} + 7x – 5 – (5x^{3} – 2x^{2} + 3x + 7)

= 7x^{3} + 7x – 5 – 5x^{3} + 2x^{2} – 3x – 7

= 2x^{3} + 2x^{2} + 4x – 12

Question 10.

How much is 3p – 4q + r less than 4p + 3q – 5r?

Solution:

Required expression

= (4p + 3q – 5r) – (3p – 4q + r)

= 4p + 3q – 5r – 3p + 4q – r

= p + 7q – 6r

Question 11.

How much is 3a^{2} – 5ab + 7b^{2} + 3 greater than 2a^{2} + 2ab + 5?

Solution:

Required expression

Question 12.

How much should 5x^{3} + 3x^{2} – 2x + 1 be increased to get 6x^{2} + 7?

Solution:

Required expression

= 6x^{2} + 7 – (5x^{3} + 3x^{2} – 2x + 1)

= 6x^{2} + 7 – 5x^{3} – 3x^{2} + 2x – 1

= -5x^{3} + 3x^{2} + 2x + 6

Question 13.

Subtract the sum of 12ab – 10b^{2} – 18a^{2} and 9ab + 12b^{2} + 14a^{2} from the sum of ab + 2b^{2} and 3b^{2} – a^{2}.

Solution:

Sum of 12ab – 10b^{2} – 18a^{2}

and 9ab + 12b^{2} + 14a^{2}

Question 14.

when a = 3, b = 0, c = -2, find the values of:

(i) ab + 2bc + 3ca + 4abc

(ii) a^{3} + b^{3} + c^{3} – 3abc

Solution:

a = 3, b = 0, c = -2

(i) ab + 2bc + 3ca + 4abc

= 3 × 0 + 2 × 0 × (-2) + 3(-2)(3) + 4(3)(0)(-2)

= 0 + 0 – 18 + 0

= -18

(ii) a^{3} + b^{3} + c^{3} – 3abc

= (3)^{3} + (0)^{3} + (-2)^{3} – 3 × 3 × 0 × (-2)

= 27 + 0 – 8 – 0

= 19

Question 15.

Write the algebraic expression for the nth term of the number pattern 13, 23, 33, 43, ………..

Solution:

13, 23, 33, 43

13 = 10 × 1 + 3

23 = 10 × 2 + 3

33 = 10 × 3 + 3

43 = 10 × 4 + 3

10 × n + 3 = 10n + 3

Where n is a natural number.