Question

$\text{Let}A=3y^2+9x-3x^2,B=6x^2-2y^2+3x,C=9x^2-3xy-y^2.\text{Find A + B - C.}$

• A. $6x^2-3xy-12x+2y^2$
• B. $-3x^2+3xy-12x+2y^2$
• C. $2x^2+xy+4x+y^2$
• D. $-6x^2+3xy+12x+2y^2$

Answer 1

The correct option is D $-6x^2+3xy+12x+2y^2$

Given:
$A=3y^2+9x-3x^2$
$B=6x^2-2y^2+3x$
$C=9x^2-3xy-y^2$
$A+B=(3y^2+9x-3x^2)+(6x^2-2y^2+3x)$
(Grouping the like terms together)
$=(3y^2-2y^2)+(9x+3x)+(-3x^2+6x^2)$
$=y^2+12x+3x^2$

Now subtracting C from (A+B),
$(A+B)-C=(y^2+12x+3x^2)-(9x^2-3xy-y^2)$
$=y^2+12x+3x^2-9x^2+3xy+y^2$
(Grouping the like terms together)
$=(y^2+y^2)+(3x^2-9x^2)+\left(3xy\right)+\left(12x\right)$
$=2y^2-6x^2+3xy+12x$

On rearranging the terms we get,
$A+B-C=-6x^2+3xy+12x+2y^2$