**Multiplying monomials by monomials worksheet :**

Here we are going to see some practice questions on multiplying monomials by monomials.

(1) Find the product of the following monomials

4ab, 3a^{2} b^{2}, 2a^{3} b^{3}

(2) Find the product of the following monomials

-7x and 3y

(3) Find the product of the following monomials

(3/7) x^{5} and (14/9) x^{2}

(4) Find the product of the following monomials

xyz and x^{2}yz

(5) Find the product of the following monomials

x^{3}y^{5} and xy^{2}

(6) Find the product of the following monomials

a^{2} b^{2} c^{3 }and abc^{2}

**Question 1 :**

Find the product of the following monomials

4ab, 3a^{2} b^{2}, 2a^{3} b^{3}

**Solution :**

**To find the product of the above monomials, first let us multiply the coefficients of the given monomials.**

= 4ab **⋅ **3a^{2} b^{2}**⋅** 2a^{3} b^{3}

= 4(3)(2) a **⋅ **a^{2 }**⋅ **a^{3 }**⋅ **b **⋅ **b^{2} **⋅ **b^{3}

= 24 a^{(1 + 2 + 3) }**⋅ **b^{(1 + 2 + 3)}

= 24 a^{6 }**⋅ **b^{6}

**Question 2 :**

Find the product of the following monomials

-7x and 3y

**Solution :**

**To find the product of the above monomials, first let us multiply the coefficients of the given monomials.**

= -7x **⋅** 3y

= -7(3) x y

= -21 xy

**Question 3 :**

Find the product of the following monomials

(3/7) x^{5} and (14/9) x^{2}

**Solution :**

**To find the product of the above monomials, first let us multiply the coefficients of the given monomials.**

= (3/7) x^{5} **⋅** (14/9) x^{2}

= (3/7) **⋅** (14/9) x^{5}**⋅**x^{2}

= (2/3) x^{(5 + 2)}

= (2/3)x^{7}

**Question 4 :**

Find the product of the following monomials

xyz and x^{2}yz

**Solution :**

**Here we don't have coefficients for any terms. So we have to combine the like terms.**

= xyz **⋅** x^{2}yz

= x ⋅ x^{2 }y ⋅ y z ⋅ z

= x^{(1+2)} y^{(1+1)}z^{(1+1) }

**= x ^{3} y^{2}z^{2 }**

**Question 5 :**

Find the product of the following monomials

x^{3}y^{5} and xy^{2}

**Solution :**

= x^{3}y^{5} **⋅ **xy^{2}

= x^{3} **⋅ **x y^{5 }**⋅ **y^{2}

= x^{(3 + 1) }y^{(5+2)}

= x^{4 }y^{7}

**Question 6 :**

Find the product of the following monomials

a^{2} b^{2} c^{3 }and abc^{2}

**Solution :**

= a^{2} b^{2} c^{3 }^{ }**⋅ ** abc^{2}

= a^{2}^{ }⋅ a b^{2 }⋅ b ⋅ c^{3 }⋅ c^{2}

= a^{(2+1)} b^{(2+1)}c^{(3+2)}

= a^{3} b^{3}c^{5}

After having gone through the stuff given above, we hope that the students would have understood "Multiplying monomials by monomials worksheet".

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