Question

What should be subtracted from $3x^2-4y^2+5xy+20$ to obtain $-x^2-y^2+6xy+20$?

• A. $3x^2+6y^2-2xy-40$
• B. $4x^2-3y^2+6xy+40$
• C. $4x^2-3y^2-xy$
• D. $3x^2+6y^2+xy$

Answer 1

The correct option is C $4x^2-3y^2-xy$

Let the expression to be subtracted be A.
$\Rightarrow (3x^2-4y^2+5xy+20)-A=(-x^2-y^2+6xy+20)$
$\Rightarrow A=(3x^2-4y^2+5xy+20)-(-x^2-y^2+6xy+20)$,
Grouping all the like terms together, we get
$A=(3x^2+x^2)+(-4y^2+y^2)+(5xy-6xy)+(20-20)$
$\Rightarrow$ $A=4x^2-3y^2-xy$.
Hence the expression that is to be subtracted is $4x^2-3y^2-xy$.