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.

Do Refer:

- Worksheet on Dividing Monomials
- Worksheet on Multiplying Binomials
- Worksheet on Multiplying Monomial and Binomial

## Multiplication of Monomials Practice Worksheet

**I. Find the product of the monomials:
**(i) 5a × 4a

(ii) 2x × 7x × 3

(iii) 3xy × 8by

(iv) x × 3x

^{2}× 4x

^{3}

(v) 5 × 3m

^{2}

(vi) 7 × 3p

^{2}× 4p

^{2}q

^{2}

(vii) (-3x) × 7x

^{2}y

(viii) (- 6x

^{2}y

^{2}) × (- 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=a^{2}

Therefore,5a.4a=20a^{2}

(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=x^{2}

Therefore, 2x × 7x × 3=42x^{2}

(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=bxy^{2}

Therefore, 3xy × 8by=24bxy^{2}

(iv) Given monomials are x, 3x^{2}, 4x^{3}

Multiply the coefficients i.e. 3 × 8=24

Multiply the variables by adding the exponents i.e. x × x^{2} × x^{3}=x^{6}

=12x^{6}

(v) Given monomials are 5 , 3m^{2
}Multiply the coefficients i.e. 5 × 3=15

=15m^{2}

(vi) Given monomials are 7, 3p^{2},4p^{2}q^{2}

Multiply the coefficients i.e. 7 × 3 × 4 =84

Multiply the variables by adding the exponents i.e. p^{2} × p^{2}q^{2}=p^{4}q^{2}

Therefore, 7 × 3p^{2} × 4p^{2}q^{2} = 84p4q^{2}

(vii) Given monomials are -3x × 7x^{2}y

Multiply the coefficients i.e. -3 × 7 =21

Multiply the variables by adding the exponents i.e. x × x^{2}y=x^{3}y

Therefore, (-3x) × 7x^{2}y =-21x^{3}y

(viii) Given monomials are (- 6x^{2}y^{2}) × (- 6xy)

Multiply the coefficients i.e. -6 × -6 =36

Multiply the variables by adding the exponents i.e. x^{2}y^{2} × xy=x^{3}y^{3}

=36x^{3}y^{3}

**II. Find the value of the following:
**(i) 15x

^{3}× 2x

^{4}

(ii) (-2m

^{4}) × 5n

^{5}

(iii) 4xyz × 2x

^{2}y

^{3}

(iv) abcd × a

^{2}b

^{2}c

(v) 4 × 3p

^{2}× 2p

^{2}q

^{2}

(vi) 0 × (15x

^{4}y

^{4}z

^{2})

**Solution:**

(i) Given 15x^{3} × 2x^{4}

Multiply the coefficients i.e. 15 × 2=30

Multiply the variables by adding the exponents i.e. x^{7}

The value of 15x^{3} × 2x^{4 } is 30x^{7}.

(ii) Given (-2m^{4}) × 5n^{5}

Multiply the coefficients i.e. -2 × 5=-10

Multiply the variables by adding the exponents i.e. m^{4} × n^{5}

The value of (-2m^{4}) × 5n^{5} is -10m^{4} × n^{5}.

(iii) Given 4xyz × 2x^{2}y^{3}

Multiply the coefficients i.e. 4 × 2=8

Multiply the variables by adding the exponents i.e. xyz × x^{2}y^{3}=x^{3}y^{4}z

The value of 4xyz × 2x^{2}y^{3} is 8x^{3}y^{4}z

(iv) Given a^{2}bc × a^{2}b^{2}c

Multiply the coefficients i.e. 1 × 1=1

Multiply the variables by adding the exponents i.e. a^{2}bc × a^{2}b^{2}c=a^{4}b^{3}c^{2}

The value of a^{2}bc × a^{2}b^{2}c is a^{4}b^{3}c^{2}

(v) Given 4 × 3p^{2} × 2p^{2}q^{2}

Multiply the coefficients i.e. 4 × 3 × 2=24

Multiply the variables by adding the exponents i.e. p^{2} × p^{2}q^{2}=p^{4}q^{2}

The value of 4 × 3p^{2} × 2p^{2}q^{2} is 24p^{4}q^{2}.

(vi) Given 0 × (15x^{4}y^{4}z^{2})

Multiply the coefficients i.e. 0 × 15=0

Multiply the variables by adding the exponents i.e. x^{4}y^{4}z^{2} is x^{4}y^{4}z^{2}

The value of 0 × (15x^{4}y^{4}z^{2}) is 0.

**III. Find the product of the following two monomials:
**(i) 10mn and -3mn

(ii) ab

^{6}and (-a

^{5}b

^{3})

(iii) 6ab and 2ac

(iv) 8mp

^{2}and 2mn

^{2}p

**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=m^{2}n^{2}

The product of the two monomials is 10mn × -3mn=-30m^{2}n^{2}.

(ii) Given two monomials are ab^{6} and (-a^{5}b^{3})

Multiply the coefficients i.e. 1. (-1)=-1.

Multiply the variables by adding the exponents i.e. ab^{6} × (a^{5}b^{3})= a^{6}b^{9}

The product of the two monomials is -a^{6}b^{9}.

(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=a^{2}bc

The product of the two monomials is 12a^{2}bc.

(iv) Given two monomials are 8mm^{2}p and 2mn^{2}

Multiply the coefficients i.e. 8 × 2=16

Multiply the variables by adding the exponents i.e. mp^{2} × mn^{2}p=m^{2}n^{2}p^{3}

The product of the two monomials is 16m^{2}n^{2}p^{3}

**IV. Find the product of the three monomials:
**(i) 15ab

^{3}c

^{5}, 3a

^{2}b

^{3}c

^{3}and 2abc

^{4}

(ii) 7mn

^{3}, 2m

^{2}n

^{2}and 3mn

^{2}

(iii) 2a

^{4}, b

^{3}a

^{5}and 12a

^{2}b

^{2}c

(iv) (-a

^{2}b

^{3}), (-5a

^{2}b) and 12a

^{2}b

**Solution:**

(i) Given three monomials are 15ab^{3}c^{5}, 3a^{2}b^{3}c^{3} and 2abc^{4}

Multiply the coefficients i.e. 15 × 3 × 2=90

Multiply the variables by adding the exponents i.e. ab^{3}c^{5} × a^{2}b^{3}c^{3} ×abc^{4}=a^{4}b^{7}c^{12}

The product of three monomials is 90a^{4}b^{7}c^{12}

(ii) Given three monomials are 7mn^{3}, 2m^{2}n^{2} and 3mn^{2
}Multiply the coefficients i.e. 7 × 2 × 3=42

Multiply the variables by adding the exponents i.e. mn^{3} × m^{2}n^{2} × mn^{2}=m^{4}n^{7}

The product of three monomials is 42m^{4}n^{7}.

(iii) Given three monomials are 2a^{4}, b^{3}a^{5} and 12a^{2}b^{2}c

Multiply the coefficients i.e. 2 × 1 × 12=24

Multiply the variables by adding the exponents i.e. a^{4} × b^{3}a^{5} × a^{2}b^{2}c=a^{11}b^{5}c

The product of three monomials is 24a^{11}b^{5}c.

(iv) Given three monomials are (-a^{2}b^{3}), (-5a^{2}b) and 12a^{2}b

Multiply the coefficients i.e. -1 × -5 × 12=60

Multiply the variables by adding the exponents i.e. a^{2}b^{3} × a^{2}b × a^{2}b=a^{6}b^{5}

The product of three monomials is 60a^{6}b^{5}.

**V. Multiply a monomial by a monomial:
**(i) 9x by 6

(ii) 5a

^{2}by 9

(iii) 16mn by 2

(iv) –mn by 18

**Solution:**

(i) Given 9x,6

9x × 6=54x

(ii) Given 5a^{2} by 9

5a2 × 9=45a2

(iii) Given 16mn by 2

16mn × 2=32mn

(iv) Given –mn by 18

–mn × 18=-18mn

** **