# Worksheet on multiplication of monomials

Q.1 Multiply

(i) 3x³ and 2x²y

(ii) -5x²y,7xy, and 3x²y²

Q.2 Multiply -3xy ,-2x²y ,-5x .Find its value by taking x=-1 ,y=1

Q.3 Find the volume of a cuboid with the following dimensions :

(i) 16 x^6,20xy²,0.6x²y²

(ii) 6xy,3xy,2x²

Q.4 Find the products and value of the given variable by taking x=-3,y=2 :

3x²y,-xy² and -xy

Solution:

Note: The product of two monomials is also a monomial

Problem: 01 Multiply

(i) 3x³ and 2x²y

(ii) -5x²y,7xy, and 3x²y²

Solution (i)

(3x³)×(2x²y)={3×2}{x³×x²}{y}

(3x³)×(2x²y)={6}{x^5}{y}

(3x³)×(2x²y)=6x^5y

Solution(ii)

(-5x²y)×(7xy)×(3x²y²)={-5×7×3}{x²×x×x²}{y×y×y²}

(-5x²y)×(7xy)×(3x²y²)={-105}{x^5}{y^4}

(-5x²y)×(7xy)×(3x²y²)=-105x^5y^4

Problem: 02  Multiply -3xy ,-2x²y ,-5x .Find its value by taking x=-1 ,y=1

Solution:

( -3xy)×(-2x²y)×(-5x)={-3×-2×-5}{x×x²×x}{y×y}

( -3xy)×(-2x²y)×(-5x)={-30}{x^4}{y²}

( -3xy)×(-2x²y)×(-5x)=-30x^4

Substitute x=-1 and y=1

= -30x^4

= -30(-1)^(1)²

= -30×1×1

= -30

Problem: 03

Find the volume of a cuboid with the following dimensions :

(i) 16 x^6,20xy²,0.6x²y²

(ii) 6xy,3xy,2x²

Solution(i):

We know ,Volume of a cuboid =length ×breadth×height

Given: Length= 16 x^6 ,breadth=20xy² and height=0.6x²y²

Volume of cuboid=(16 x^6)×(20xy²)×(0.6x²y²)

Volume of cuboid={16×20×0.6}{x^6×x×x²}{y²×y²}

Volume of cuboid=192x^8y^4

Solution(ii):

Given: Length= 6xy ,breadth=3xy,and height=2x²

Volume of cuboid= (6xy)×( 3xy)×(2x²)

Volume of cuboid={6×3×2}{x×x×x²}{y×y}

Volume of cuboid=36x^4

Problem: 04

Find the products and value of the given variable by taking x=-3,y=2 :

3x²y,-xy² and -xy

Solution:

(3x²y)×(-xy²)×(-xy )={3×-1×-1}{x²×x×x}{y×y²×y}

(3x²y)×(-xy²)×(-xy )={3}{x^4}{y^4}

(3x²y)×(-xy²)×(-xy )= 3(x^4)(y^4

Substitute x=-3 and y=2

=3(x^4)(y^4

=3(-3)^4(2^4)

=3×81×16

=3888

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