Solve (sqrt{2}a-3sqrt{b})(sqrt{2}a+3sqrt{b})

$$( \sqrt { 2 } a - 3 \sqrt { b } ) ( \sqrt { 2 } a + 3 \sqrt { b } )$$

Evaluate

$$2a^{2}-9b$$

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}.

$$\left(\sqrt{2}a\right)^{2}-\left(3\sqrt{b}\right)^{2}$$

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

$$\left(\sqrt{2}\right)^{2}a^{2}-\left(3\sqrt{b}\right)^{2}$$

The square of \sqrt{2} is 2.

$$2a^{2}-\left(3\sqrt{b}\right)^{2}$$

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

$$2a^{2}-3^{2}\left(\sqrt{b}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$2a^{2}-9\left(\sqrt{b}\right)^{2}$$

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

$$2a^{2}-9b$$

Differentiate w.r.t. a

$$4a$$