How do you combine like terms in #(- 7x ^ { 5} y ^ { 6} - 3x ^ { 6} y ^ { 5} + 9x y ) + ( - 3x ^ { 6} y ^ { 5} + 5x y - 3x ^ { 5} y ^ { 6} )#?

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Answer 1 · 2017-08-26T02:09:47

See a solution process below:

First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

#-7color(red)(x^5y^6) - 3color(blue)(x^6y^5) + 9color(orange)(xy) - 3color(blue)(x^6y^5) + 5color(orange)(xy) - 2color(red)(x^5y^6)#

Next, group like terms:

#-7color(red)(x^5y^6) - 2color(red)(x^5y^6) - 3color(blue)(x^6y^5) - 3color(blue)(x^6y^5) + 9color(orange)(xy) + 5color(orange)(xy)#

Now, combine like terms:

#(-7 - 2)color(red)(x^5y^6) + (-3 - 3)color(blue)(x^6y^5) + (9 + 5)color(orange)(xy)#

#-9color(red)(x^5y^6) + (-6)color(blue)(x^6y^5) + 14color(orange)(xy)#

#-9color(red)(x^5y^6) - 6color(blue)(x^6y^5) + 14color(orange)(xy)#