Solve (4sqrt{5}+sqrt{3})(4sqrt{5}-sqrt{3})

$$( 4 \sqrt { 5 } + \sqrt { 3 } ) ( 4 \sqrt { 5 } - \sqrt { 3 } )$$

Evaluate

$$77$$

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}.

$$\left(4\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}$$

Expand \left(4\sqrt{5}\right)^{2}.

$$4^{2}\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{5} is 5.

$$16\times 5-\left(\sqrt{3}\right)^{2}$$

Multiply 16 and 5 to get 80.

$$80-\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$80-3$$

Subtract 3 from 80 to get 77.

$$77$$

Factor

$$7\times 11$$