To multiply two or more monomials, we have to follow the rule given below.
(i) Multiply the signs
(ii) Multiply the coefficients
(iii) Multiply the variables.
Problem 1 :
(3x²) (7x³)
Solution :
= (3x²) (7x³)
Multiplying the coefficients and multiplying variables together, we get
= (3 ∙ 7) (x² ∙ x³)
Use the product of power property.
= 21x^{2+3}
= 21x^{5}
Problem 2 :
8m^{5 }∙ m
Solution :
= 8m^{5 }∙ m
Multiplying the coefficients and multiplying variables together, we get
= (8 ∙ 1) (m^{5} ∙ m^{1})
Use the product of power property.
= 8m^{5+1}
= 8m^{6}
Problem 3 :
t³ ∙ 6t^{7}
Solution :
= t³ ∙ 6t^{7}
Group factors with like bases together.
= (1 ∙ 6) (t³ ∙ t^{7})
Multiplying the coefficients and multiplying variables together, we get
Use the product of power property.
= 6t^{3+7}
= 6t^{10}
Problem 4 :
(4y^{4}) (-9y²)
Solution :
= (4y^{4}) (-9y²)
Multiplying the coefficients and multiplying variables together, we get
= (4 ∙ -9) (y^{4} ∙ y²)
Use the product of power property.
= - 36y^{4+2}
= - 36y^{6}
Problem 5 :
3r^{5} ∙ 2r² ∙7r^{6}
Solution :
= 3r^{5} ∙ 2r² ∙7r^{6}
Multiplying the coefficients and multiplying variables together, we get
= (3 ∙ 2 ∙ 7) (r^{5} ∙ r² ∙ r^{6})
Use the product of power property.
= 42r^{5+2+6}
= 42r^{13}
Problem 6 :
(-2p³r) (11r^{4}p^{6})
Solution :
= (-2p³r) (11r^{4}p^{6})
Multiplying the coefficients and multiplying variables together, we get
= (-2 ∙ 11) (p³ ∙ p^{6} ∙ r ∙ r^{4})
Use the product of power property.
= -22p^{ (3+6) }r^{ (1+4)}
= -22p^{9}r^{5}
Problem 7 :
(6y³x) (5y³)
Solution :
= (6y³x) (5y³)
Multiplying the coefficients and multiplying variables together, we get
= (6 ∙ 5) (x ∙ y³ ∙ y³)
Use the product of power property.
= 30xy^{3+3}
= 30xy^{6}
Problem 8 :
7c^{5}a³b ∙ 8a²b^{4}c
Solution :
= 7c^{5}a³b ∙ 8a²b^{4}c
Multiplying the coefficients and multiplying variables together, we get
= (7 ∙ 8) (a³ ∙ a² ∙ b ∙ b^{4} ∙ c^{5} ∙ c)
Use the product of power property.
= (7 ∙ 8) (a ^{(2+3) }b ^{(1+4) }c ^{(5+1)})
= 56a^{5}b^{5}c^{6}
Problem 9 :
(-3t³u²) (-4u³t)
Solution :
= (-3t³u²) (-4u³t)
Multiplying the coefficients and multiplying variables together, we get
= (-3 ∙ -4) (t³ ∙ t ∙ u² ∙ u³)
Use the product of power property.
= (-3 ∙ -4) (t ^{(3+1) }u ^{(2+3)})
= 12t^{4}u^{5}
Problem 10 :
9/4 z^{6} × 4/27 z^{7} × 1/2 z²
Solution :
= 9/4 z^{6} × 4/27 z^{7} × 1/2 z²
Multiplying the coefficients and multiplying variables together, we get
= (9/4 ∙ 4/27 ∙ 1/2) (z^{6} ∙ z^{7} ∙ z²)
Use the product of power property.
= 1/6 z ^{(6+7+2)}
= 1/6 z^{15}
Problem 11 :
-5/7 q^{4} × -7/5 q^{6}
Solution :
= -5/7 q^{4} × -7/5 q^{6}
Multiplying the coefficients and multiplying variables together, we get
= (-5/7 ∙ -7/5) (q^{4} ∙ q^{6})
Use the product of power property.
= 1 ∙ q^{4+6}
= q^{10}
Problem 12 :
6v² × -8v^{7}
Solution :
= 6v² × -8v^{7}
Group factors with like bases together.
= (6 ∙ -8) (v² ∙ v^{7})
Use the product of power property.
= - 48v^{2+7}
= - 48v^{9}
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM