Strengthen your basics in algebra by practicing the numerous questions from the Worksheet on Multiplying Monomials. Solve Algebraic Expressions fluently by attempting the Multiplication of Monomials Worksheet over here. The Printable Math Worksheet on Multiplication of Monomials will give constructive engagement and ample practice for the theories revolving around the monomials. Practice the Multiplying Monomials Worksheet with Answers in PDF Formats for free and identify the different types of algebraic expressions.

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Multiplication of Monomials Practice Worksheet

I. Find the product of the monomials:
(i) 5a × 4a
(ii) 2x × 7x × 3
(iii) 3xy × 8by
(iv) x × 3x2 × 4x3
(v) 5 × 3m2
(vi) 7 × 3p2 × 4p2q2
(vii) (-3x) × 7x2y
(viii) (- 6x2y2) × (- 6xy)

Solution:

(i) Given monomials are 5a,4a.
Multiply the coefficients i.e. 4 × 5=20
Multiply the variables by adding the exponents i.e. a.a=a2
Therefore,5a.4a=20a2
(ii) Given monomials are 2x , 7x,  3
Multiply the coefficients i.e. 2 ×  7 × 3=42
Multiply the variables by adding the exponents i.e. x × x=x2
Therefore, 2x × 7x × 3=42x2
(iii) Given monomials are 3xy , 8by
Multiply the coefficients i.e. 3 × 8=24
Multiply the variables by adding the exponents i.e. xy × by=bxy2
Therefore, 3xy × 8by=24bxy2
(iv) Given monomials are x, 3x2, 4x3
Multiply the coefficients i.e. 3 × 8=24
Multiply the variables by adding the exponents i.e. x × x2 × x3=x6
=12x6
(v) Given monomials are 5 , 3m2
Multiply the coefficients i.e. 5 × 3=15
=15m2
(vi) Given monomials are 7, 3p2,4p2q2
Multiply the coefficients i.e. 7 × 3 × 4 =84
Multiply the variables by adding the exponents i.e. p2 × p2q2=p4q2
Therefore, 7 × 3p2 × 4p2q2 = 84p4q2
(vii) Given monomials are -3x × 7x2y
Multiply the coefficients i.e. -3 × 7 =21
Multiply the variables by adding the exponents i.e. x × x2y=x3y
Therefore, (-3x) × 7x2y =-21x3y
(viii) Given monomials are (- 6x2y2) × (- 6xy)
Multiply the coefficients i.e. -6 × -6 =36
Multiply the variables by adding the exponents i.e. x2y2 × xy=x3y3
=36x3y3

II. Find the value of the following:
(i) 15x3 × 2x4
(ii) (-2m4) × 5n5
(iii) 4xyz × 2x2y3
(iv) abcd × a2b2c
(v) 4 × 3p2 × 2p2q2
(vi) 0 × (15x4y4z2)

Solution:

(i) Given 15x3 × 2x4
Multiply the coefficients i.e. 15 × 2=30
Multiply the variables by adding the exponents i.e. x7
The value of 15x3 × 2x is 30x7.

(ii) Given (-2m4) × 5n5
Multiply the coefficients i.e. -2 × 5=-10
Multiply the variables by adding the exponents i.e. m4 × n5
The value of (-2m4) × 5n5 is -10m4 × n5.
(iii) Given 4xyz × 2x2y3
Multiply the coefficients i.e. 4 × 2=8
Multiply the variables by adding the exponents i.e. xyz × x2y3=x3y4z
The value of 4xyz × 2x2y3 is 8x3y4z

(iv) Given a2bc × a2b2c
Multiply the coefficients i.e. 1 × 1=1
Multiply the variables by adding the exponents i.e. a2bc × a2b2c=a4b3c2
The value of a2bc × a2b2c is a4b3c2
(v) Given 4 × 3p2 × 2p2q2
Multiply the coefficients i.e. 4 × 3 × 2=24
Multiply the variables by adding the exponents i.e. p2 × p2q2=p4q2
The value of 4 × 3p2 × 2p2q2 is 24p4q2.
(vi) Given 0 × (15x4y4z2)
Multiply the coefficients i.e. 0 × 15=0
Multiply the variables by adding the exponents i.e. x4y4z2 is x4y4z2
The value of 0 × (15x4y4z2) is 0.

III. Find the product of the following two monomials:
(i) 10mn and -3mn
(ii) ab6 and (-a5b3)
(iii) 6ab and 2ac
(iv) 8mp2 and 2mn2p

Solution:

(i) Given two monomials are 10mn and -3mn
Multiply the coefficients i.e. 10 × -3 =-30
Multiply the variables by adding the exponents i.e. mn × mn=m2n2
The product of the two monomials is 10mn × -3mn=-30m2n2.

(ii) Given two monomials are ab6 and (-a5b3)
Multiply the coefficients i.e. 1. (-1)=-1.
Multiply the variables by adding the exponents i.e. ab6 × (a5b3)= a6b9
The product of the two monomials is -a6b9.

(iii) Given two monomials are 6ab and 2ac
Multiply the coefficients i.e. 6 × 2=12
Multiply the variables by adding the exponents i.e. ab × ac=a2bc
The product of the two monomials is 12a2bc.

(iv) Given two monomials are 8mm2p and 2mn2
Multiply the coefficients i.e. 8 × 2=16
Multiply the variables by adding the exponents i.e. mp2 × mn2p=m2n2p3
The product of the two monomials is 16m2n2p3

IV. Find the product of the three monomials:
(i) 15ab3c5, 3a2b3c3 and 2abc4
(ii) 7mn3, 2m2n2 and 3mn2
(iii) 2a4, b3a5 and 12a2b2c
(iv) (-a2b3), (-5a2b) and 12a2b

Solution:

(i) Given three monomials are 15ab3c5, 3a2b3c3 and 2abc4
Multiply the coefficients i.e. 15 × 3 × 2=90
Multiply the variables by adding the exponents i.e. ab3c5 × a2b3c3 ×abc4=a4b7c12
The product of three monomials is 90a4b7c12

(ii) Given three monomials are 7mn3, 2m2n2 and 3mn2
Multiply the coefficients i.e. 7 × 2 × 3=42
Multiply the variables by adding the exponents i.e. mn3 × m2n2 × mn2=m4n7
The product of three monomials is 42m4n7.

(iii) Given three monomials are 2a4, b3a5 and 12a2b2c
Multiply the coefficients i.e. 2 × 1 × 12=24
Multiply the variables by adding the exponents i.e. a4 × b3a5 × a2b2c=a11b5c
The product of three monomials is 24a11b5c.

(iv) Given three monomials are (-a2b3), (-5a2b) and 12a2b
Multiply the coefficients i.e. -1 × -5 × 12=60
Multiply the variables by adding the exponents i.e. a2b3 × a2b × a2b=a6b5
The product of three monomials is 60a6b5.

V. Multiply a monomial by a monomial:
(i) 9x by 6
(ii) 5a2 by 9
(iii) 16mn by 2
(iv) –mn by 18

Solution:

(i) Given 9x,6
9x × 6=54x
(ii) Given 5a2 by 9
5a2 × 9=45a2
(iii) Given 16mn by 2
16mn × 2=32mn
(iv) Given –mn by 18
–mn × 18=-18mn