How do you combine like terms in #(3x ^ { 2} y ^ { 3} + x ^ { 2} - 4x ^ { 3} y ^ { 2} ) - ( 2x ^ { 3} y ^ { 2} - 7y ^ { 3} + 5x ^ { 2} )#?

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Answer 1 · 2017-08-18T02:35:20

See a solution process below:

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

#3x^2y^3 + x^2 - 4x^3y^2 - 2x^3y^2 + 7y^3 - 5x^2#

Next, group like terms:

#3x^2y^3 + x^2 - 5x^2 + 7y^3 - 4x^3y^2 - 2x^3y^2#

Now, combine like terms:

#3x^2y^3 + 1x^2 - 5x^2 + 7y^3 - 4x^3y^2 - 2x^3y^2#

#3x^2y^3 + (1 - 5)x^2 + 7y^3 + (-4 - 2)x^3y^2#

#3x^2y^3 + (-4)x^2 + 7y^3 + (-6)x^3y^2#

#3x^2y^3 - 4x^2 + 7y^3 - 6x^3y^2#