MULTIPLYING  MONOMIALS

Example 1 :

Multiply. 

(4y²)(5y³)

Solution :

=  (4y²)(5y³)

Group factors with like bases together. 

=  (4 ⋅ 5)(y² ⋅ y³)

Use the Product of Powers Property. 

=  20y^{2 + 3}

=  20y⁵

Example 2 :

Find the product of the following monomials.

-5x and 3y

Solution :

=  -5x ⋅ 3y

  =  -(5 ⋅ 3)xy

  =  -15xy

Example 3 :

Find the product of the following monomials.

(³⁄₇)x⁵ and (¹⁴⁄₉)x²

Solution :

= (³⁄₇)x⁵ ⋅ (¹⁴⁄₉)x²

Group factors with like bases together. 

=  (³⁄₇ ⋅ ¹⁴⁄₉)(x⁵ ⋅ x²)

Use the Product of Powers Property. 

=  (¹⁄₁ ⋅ ⅔)(x^{5 + 2})

=  (⅔)x⁷ 

Example 4 :

Find the product of the following monomials.

xyz and x²yz

Solution :

=  xyz ⋅  x²yz

Group factors with like bases together. 

=  (x ⋅ x²)(y ⋅ y)(z ⋅ z)

Use the Product of Powers Property. 

=  (x^{1 + 2})(y^{1 + 1})(z^{1 + 1})

=  (x³)(y²)(z²)

=  x³y²z²

Example 5 :

Find the product of the following monomials

x³y⁵ and xy²

Solution :

=  x³y⁵ ⋅  xy²

Group factors with like bases together. 

=  (x³ ⋅ x)(y⁵ ⋅ y²)

Use the Product of Powers Property. 

=  (x^{3 + 1})(y^{5 + 2})

=  (x⁴)(y⁷)

=  x⁴y⁷

Example 6 :

Find the product of the following monomials.

a²b²c³ and abc²

Solution :

=  a²b²c³ ⋅  abc²

Group factors with like bases together. 

=  (a² ⋅ a)(b² ⋅ b)(c³ ⋅ c²)

Use the Product of Powers Property. 

=  (a^{2 + 1})(b^{2 + 1})(c^{3 + 2})

=  (a³)(b³)(c⁵)

=  a³b³c⁵

Example 7 :

Find the product of the following monomials.

4ab, 3a²b² and 2a³b³

Solution :

=  4ab ⋅ 3a²b²⋅ 2a³ b³

Group factors with like bases together. 

=  (4 ⋅ 3 ⋅ 2)(a ⋅ a² ⋅ a³)(b ⋅ b² ⋅ b³)

Use the Product of Powers Property. 

=  (24)(a^{1 + 2 + 3})(b^{1 + 2 + 3})

=  24a⁶b⁶

Example 8 :

Find the product of the following monomials.

-5pq, 2p²q and -4q⁵

Solution :

=  -5pq ⋅ 2p²q ⋅ -4q⁵

Group factors with like bases together. 

=  -(5 ⋅ 2 ⋅ -4)(p ⋅ p²)(q ⋅ q ⋅ q⁵)

Use the Product of Powers Property. 

=  -(-40)p^{1 + 2}q^{1 + 1 + 5}

=  40p³q⁷

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