Solve (7sqrt{2}-5)(7sqrt{2}+5)

$$( 7 \sqrt { 2 } - 5 ) ( 7 \sqrt { 2 } + 5 )$$

Evaluate

$$73$$

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}.

$$\left(7\sqrt{2}\right)^{2}-5^{2}$$

Expand \left(7\sqrt{2}\right)^{2}.

$$7^{2}\left(\sqrt{2}\right)^{2}-5^{2}$$

Calculate 7 to the power of 2 and get 49.

$$49\left(\sqrt{2}\right)^{2}-5^{2}$$

The square of \sqrt{2} is 2.

$$49\times 2-5^{2}$$

Multiply 49 and 2 to get 98.

$$98-5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$98-25$$

Subtract 25 from 98 to get 73.

$$73$$

Factor

$$73$$