How do you multiply #( 2x ^ { 3} y ^ { 5} ) ( 6x ^ { 2} - 7y ^ { 3} )#?

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Answer 1 · 2018-03-04T09:11:01

#12x^5y^5-14x^3y^8#

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# #
#(2x^3y^5)(6x^2-7y^3)#

Remove the parantheses from the left side term as #\ \ (a)=a\ \ # to get:

#=2x^3y^5(6x^2-7y^3)#

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Apply the distributive property of multiplication #\ \ a(b+c)=ab+ac\ \ # to get our expression as:

#=2x^3y^5\cdot 6x^2+2x^3y^5(-7y^3)#
# #

Apply the minus-plus rule for parantheses #\ \ +(-a)=-a\ \ # so as to get:

#=2x^3y^5\cdot 6x^2-2x^3y^5\cdot 7y^3#

#=12x^3x^2y^5-14x^3y^5y^3#

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Apply the exponent rule #\ \ a^b\cdot a^c=a^{b+c}\ \ # to combine the like terms.

#x^3x^2= x^{3+2}= x^5# #" "# and #" "# #y^5y^3= y^{5+3}= y^8#

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So that our expression now becomes:

#=12x^5y^5-14x^3y^8#

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That's it!