Solve (1-8sqrt{2})(1+8sqrt{2})

$$( 1 - 8 \sqrt { 2 } ) ( 1 + 8 \sqrt { 2 } )$$

Evaluate

$$-127$$

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}.

$$1^{2}-\left(8\sqrt{2}\right)^{2}$$

Calculate 1 to the power of 2 and get 1.

$$1-\left(8\sqrt{2}\right)^{2}$$

Expand \left(8\sqrt{2}\right)^{2}.

$$1-8^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$1-64\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$1-64\times 2$$

Multiply 64 and 2 to get 128.

$$1-128$$

Subtract 128 from 1 to get -127.

$$-127$$

Factor

$$-127$$