Solve (3sqrt{2}+8)(3sqrt{2}-8)

$$(3 \sqrt{ 2 } +8)(3 \sqrt{ 2 } -8)$$

Evaluate

$$-46$$

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}.

$$\left(3\sqrt{2}\right)^{2}-8^{2}$$

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

$$3^{2}\left(\sqrt{2}\right)^{2}-8^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{2}\right)^{2}-8^{2}$$

The square of \sqrt{2} is 2.

$$9\times 2-8^{2}$$

Multiply 9 and 2 to get 18.

$$18-8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$18-64$$

Subtract 64 from 18 to get -46.

$$-46$$

Factor

$$-46$$