act-dog

A. Correct. First, apply the distributive property: $\left(x^2-y^2\right)-\left(6x^2+4xy-y^2\right)=x^2-y^2-6x^2-4xy+y^2$. Next, group like terms to get $x^2-6x^2-4xy-y^2+y^2$. Finally, combine like terms to get $-5x^2-4xy$.

B. Incorrect. When applying the distributive property, be sure that the negative gets distributed to all terms of the trinomial: $\left(x^2-y^2\right)-\left(6x^2+4xy-y^2\right)=x^2-y^2-6x^2-4xy+y^2$. You may not have multiplied the last 2 terms by $-1$.

C. Incorrect. Be sure to apply the distributive property to distribute the negative through the trinomial: $\left(x^2-y^2\right)-\left(6x^2+4xy-y^2\right)=x^2-y^2-6x^2-4xy+y^2$. You may have ignored the negative sign and thus calculated $x^2-y^2+6x^2+4xy-y^2$ or $7x^2+4xy-2y^2$.

D. Incorrect. Be careful with the signs when applying the distributive property. You may have used a plus sign wherever there was a minus sign to get $x^2+y^2+6x^2+4xy+y^2$ or $7x^2+4xy+2y^2$.