Solve (10sqrt{2}+14)(10sqrt{2}-14)

$$(10 \sqrt{ 2 } +14)(10 \sqrt{ 2 } -14)$$

Evaluate

$$4$$

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}.

$$\left(10\sqrt{2}\right)^{2}-14^{2}$$

Expand \left(10\sqrt{2}\right)^{2}.

$$10^{2}\left(\sqrt{2}\right)^{2}-14^{2}$$

Calculate 10 to the power of 2 and get 100.

$$100\left(\sqrt{2}\right)^{2}-14^{2}$$

The square of \sqrt{2} is 2.

$$100\times 2-14^{2}$$

Multiply 100 and 2 to get 200.

$$200-14^{2}$$

Calculate 14 to the power of 2 and get 196.

$$200-196$$

Subtract 196 from 200 to get 4.

$$4$$

Factor

$$2^{2}$$