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

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

Evaluate

$$4a-2b$$

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{a}\right)^{2}-\left(\sqrt{2b}\right)^{2}$$

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

$$4a-\left(\sqrt{2b}\right)^{2}$$

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

$$4a-2b$$

Differentiate w.r.t. a

$$4$$