Solve (3sqrt{x}-2sqrt{y})(3sqrt{x}+2sqrt{y})

$$( 3 \sqrt { x } - 2 \sqrt { y } ) ( 3 \sqrt { x } + 2 \sqrt { y } )$$

Evaluate

$$9x-4y$$

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}.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

$$9x-4\left(\sqrt{y}\right)^{2}$$

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

$$9x-4y$$

Differentiate w.r.t. x

$$9$$