Solve (sqrt{x}+3sqrt{y})(sqrt{x}-3sqrt{y})

$$( \sqrt { x } + 3 \sqrt { y } ) ( \sqrt { x } - 3 \sqrt { y } )$$

Evaluate

$$x-9y$$

Solution Steps

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

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

Calculate \sqrt{x} to the power of 2 and get x.

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

Expand \left(3\sqrt{y}\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

$$x-9\left(\sqrt{y}\right)^{2}$$

Calculate \sqrt{y} to the power of 2 and get y.

$$x-9y$$

Differentiate w.r.t. x

$$1$$