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Question

Let A=3y2+9x−3x2,B=6x2−2y2+3x,C=9x2−3xy−y2. Find A + B - C.

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Solution

Given:
A=3y2+9x−3x2
B=6x2−2y2+3x
C=9x2−3xy−y2
A+B=(3y2+9x−3x2)+(6x2−2y2+3x)
(Grouping the like terms together)
=(3y2−2y2)+(9x+3x)+(−3x2+6x2)
=y2+12x+3x2

Now subtracting C from (A+B),
(A+B)−C=(y2+12x+3x2)−(9x2−3xy−y2)
=y2+12x+3x2−9x2+3xy+y2
(Grouping the like terms together)
=(y2+y2)+(3x2−9x2)+(3xy)+(12x)
=2y2−6x2+3xy+12x

On rearranging the terms we get,
A+B−C=−6x2+3xy+12x+2y2

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