How do you solve #2a ^ { 2} ( 10a ^ { 3} + 5a )#?

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Answer 1 · 2017-06-28T21:09:03

See a solution process below:

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

#color(red)(2a^2)(10a^3 + 5a) => (color(red)(2a^2) xx 10a^3) + color(red)(2a^2) xx 5a) =>#

#((2 xx 10) xx (a^2 xx a^3)) + ((2 xx 5) xx (a^2 xx a)) =>#

#20(a^2 xx a^3) + 10(a^2 xx a)#

Now, we can use these two rules of exponents to multiply each set of #a# terms:

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

#20(a^2 xx a^3) + 10(a^2 xx a) => 20(a^color(red)(2) xx a^color(blue)(3)) + 10(a^color(red)(2) xx a^color(blue)(1)) =>#

#20a^(color(red)(2)+color(blue)(3)) + 10a^(color(red)(2)+color(blue)(1)) =>#

#20a^5 + 10a^3#