Solve (sqrt{7}+4sqrt{3})(sqrt{7}-4sqrt{3})

$$( \sqrt { 7 } + 4 \sqrt { 3 } ) ( \sqrt { 7 } - 4 \sqrt { 3 } )$$

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}.

$$\left(\sqrt{7}\right)^{2}-\left(4\sqrt{3}\right)^{2}$$

The square of \sqrt{7} is 7.

$$7-\left(4\sqrt{3}\right)^{2}$$

Expand \left(4\sqrt{3}\right)^{2}.

$$7-4^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$7-16\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$7-16\times 3$$

Multiply 16 and 3 to get 48.

$$7-48$$

Subtract 48 from 7 to get -41.

$$-41$$

Factor

$$-41$$