Solve (5sqrt{2}-3)(5sqrt{2}+3)

$$(5 \sqrt{ 2 } -3)(5 \sqrt{ 2 } +3)$$

Evaluate

$$41$$

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}.

$$\left(5\sqrt{2}\right)^{2}-3^{2}$$

Expand \left(5\sqrt{2}\right)^{2}.

$$5^{2}\left(\sqrt{2}\right)^{2}-3^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25\left(\sqrt{2}\right)^{2}-3^{2}$$

The square of \sqrt{2} is 2.

$$25\times 2-3^{2}$$

Multiply 25 and 2 to get 50.

$$50-3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$50-9$$

Subtract 9 from 50 to get 41.

$$41$$

Factor

$$41$$