Solve (sqrt{5}+4sqrt{7})(sqrt{5}-4sqrt{7})

$$( \sqrt { 5 } + 4 \sqrt { 7 } ) ( \sqrt { 5 } - 4 \sqrt { 7 } )$$

Evaluate

$$-107$$

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}.

$$\left(\sqrt{5}\right)^{2}-\left(4\sqrt{7}\right)^{2}$$

The square of \sqrt{5} is 5.

$$5-\left(4\sqrt{7}\right)^{2}$$

Expand \left(4\sqrt{7}\right)^{2}.

$$5-4^{2}\left(\sqrt{7}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$5-16\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$5-16\times 7$$

Multiply 16 and 7 to get 112.

$$5-112$$

Subtract 112 from 5 to get -107.

$$-107$$

Factor

$$-107$$