Solve (8-5sqrt{3})(8+5sqrt{3})

$$( 8 - 5 \sqrt { 3 } ) ( 8 + 5 \sqrt { 3 } )$$

Evaluate

$$-11$$

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}.

$$8^{2}-\left(5\sqrt{3}\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$64-\left(5\sqrt{3}\right)^{2}$$

Expand \left(5\sqrt{3}\right)^{2}.

$$64-5^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$64-25\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$64-25\times 3$$

Multiply 25 and 3 to get 75.

$$64-75$$

Subtract 75 from 64 to get -11.

$$-11$$

Factor

$$-11$$