Solve (4sqrt{2}-sqrt{14})(4sqrt{2}+sqrt{14})

$$( 4 \sqrt { 2 } - \sqrt { 14 } ) ( 4 \sqrt { 2 } + \sqrt { 14 } )$$

Evaluate

$$18$$

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}.

$$\left(4\sqrt{2}\right)^{2}-\left(\sqrt{14}\right)^{2}$$

Expand \left(4\sqrt{2}\right)^{2}.

$$4^{2}\left(\sqrt{2}\right)^{2}-\left(\sqrt{14}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{2}\right)^{2}-\left(\sqrt{14}\right)^{2}$$

The square of \sqrt{2} is 2.

$$16\times 2-\left(\sqrt{14}\right)^{2}$$

Multiply 16 and 2 to get 32.

$$32-\left(\sqrt{14}\right)^{2}$$

The square of \sqrt{14} is 14.

$$32-14$$

Subtract 14 from 32 to get 18.

$$18$$

Factor

$$2\times 3^{2}$$