How do you simplify #(y ^ { 4} + 3y ^ { 2} - 6y + 3) - ( 5y ^ { 3} + 8y ^ { 2} - 6y )#?

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Answer 1 · 2017-09-05T13:16:56

See a solution process below:

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

#y^4 + 3color(red)(y^2) - 6color(blue)(y) + 3 - 5y^3 - 8color(red)(y^2) + 6color(blue)(y)#

Next, group like terms:

#y^4 - 5y^3 + 3color(red)(y^2) - 8color(red)(y^2) - 6color(blue)(y) + 6color(blue)(y) + 3#

Now, combine like terms:

#y^4 - 5y^3 + (3 - 8)color(red)(y^2) + (-6 + 6)color(blue)(y) + 3#

#y^4 - 5y^3 + (-5)color(red)(y^2) + (0)color(blue)(y) + 3#

#y^4 - 5y^3 - 5color(red)(y^2) + 3#