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

1 Answer
Mar 4, 2018

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

Explanation:


(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)


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

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

So that our expression now becomes:

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

That's it!