Question

$\text{What should be subtracted from}2x^2-4y^2+6xy+10\text{to obtain}-2x^2-3y^2+6xy+10?$

• A. $4x^2-y^2+20$
• B. $4x^2-y^2-20$
• C. $4x^2-y^2$
• D. $4x^2-2y^2$

Answer 1

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

Let the expression to be subtracted be $A$.

$\Rightarrow (2x^2-4y^2+6xy+10)-A=-2x^2-3y^2+6xy+10$

$\Rightarrow A=(2x^2-4y^2+6xy+10)-(-2x^2-3y^2+6xy+10)$

Grouping the like terms together,
$\Rightarrow A=(2x^2+2x^2)+(-4y^2+3y^2)+(6xy-6xy)+(10-10)$

$\Rightarrow$ $A=4x^2-y^2$

Hence, the expression that needs to be subracted is $4x^2-y^2$.