Solve (xy+4)(xy-4)+16+x^2y^2

$$( x y + 4 ) ( x y - 4 ) + 16 + x ^ { 2 } y ^ { 2 }$$

Evaluate

$$2\left(xy\right)^{2}$$

Solution Steps

Consider \left(xy+4\right)\left(xy-4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 4.

$$\left(xy\right)^{2}-16+16+x^{2}y^{2}$$

Expand \left(xy\right)^{2}.

$$x^{2}y^{2}-16+16+x^{2}y^{2}$$

Add -16 and 16 to get 0.

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

Combine x^{2}y^{2} and x^{2}y^{2} to get 2x^{2}y^{2}.

$$2x^{2}y^{2}$$

Expand

$$2\left(xy\right)^{2}$$

Solution Steps

Consider \left(xy+4\right)\left(xy-4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 4.

$$\left(xy\right)^{2}-16+16+x^{2}y^{2}$$

Expand \left(xy\right)^{2}.

$$x^{2}y^{2}-16+16+x^{2}y^{2}$$

Add -16 and 16 to get 0.

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

Combine x^{2}y^{2} and x^{2}y^{2} to get 2x^{2}y^{2}.

$$2x^{2}y^{2}$$