How do you multiply #6x y ( 6x ^ { 2} y ^ { 2} + 2y ^ { 2} + x y )#?

1 Answer
smendyka
Jan 14, 2018

See a solution process below:

Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

#color(red)(6xy)(6x^2y^2 + 2y^2 + xy) =>#

#(color(red)(6xy) xx 6x^2y^2) + (color(red)(6xy) xx 2y^2) + (color(red)(6xy) xx xy) =>#

#(36xy xx x^2y^2) + (12xy xx y^2) + (6xy xx xy)#

Now, use these rules for exponents to multiply the remaining terms:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#(36x^color(red)(1)y^color(red)(1) xx x^color(blue)(2)y^color(blue)(2)) + (12x^color(red)(1)y^color(red)(1) xx y^color(blue)(2)) + (6x^color(red)(1)y^color(red)(1) xx x^color(blue)(1)y^color(blue)(1)) =>#

#36x^(color(red)(1)+color(blue)(2))y^(color(red)(1)+color(blue)(2)) + 12x^1y^(color(red)(1)+color(blue)(2)) + 6x^(color(red)(1)+color(blue)(1))y^(color(red)(1)+color(blue)(1)) =>#

#36x^3y^3 + 12xy^3 + 6x^2y^2#

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