Solve (x^2-y^2)-[(x+y)(x-y)]+3x^2=

$$( x ^ { 2 } - y ^ { 2 } ) - [ ( x + y ) ( x - y ) ] + 3 x ^ { 2 } =$$

Evaluate

$$3x^{2}$$

Solution Steps

Consider \left(x+y\right)\left(x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x^{2}-y^{2}-\left(x^{2}-y^{2}\right)+3x^{2}$$

To find the opposite of x^{2}-y^{2}, find the opposite of each term.

$$x^{2}-y^{2}-x^{2}+y^{2}+3x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$-y^{2}+y^{2}+3x^{2}$$

Combine -y^{2} and y^{2} to get 0.

$$0+3x^{2}$$

Anything plus zero gives itself.

$$3x^{2}$$

Expand

$$3x^{2}$$

Solution Steps

Consider \left(x+y\right)\left(x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x^{2}-y^{2}-\left(x^{2}-y^{2}\right)+3x^{2}$$

To find the opposite of x^{2}-y^{2}, find the opposite of each term.

$$x^{2}-y^{2}-x^{2}+y^{2}+3x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$-y^{2}+y^{2}+3x^{2}$$

Combine -y^{2} and y^{2} to get 0.

$$0+3x^{2}$$

Anything plus zero gives itself.

$$3x^{2}$$