Solve (4sqrt{5}-3sqrt{7})(4sqrt{5}+3sqrt{7})=

$$( 4 \sqrt { 5 } - 3 \sqrt { 7 } ) ( 4 \sqrt { 5 } + 3 \sqrt { 7 } ) =$$

Evaluate

$$17$$

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}.

$$\left(4\sqrt{5}\right)^{2}-\left(3\sqrt{7}\right)^{2}$$

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

$$4^{2}\left(\sqrt{5}\right)^{2}-\left(3\sqrt{7}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{5}\right)^{2}-\left(3\sqrt{7}\right)^{2}$$

The square of \sqrt{5} is 5.

$$16\times 5-\left(3\sqrt{7}\right)^{2}$$

Multiply 16 and 5 to get 80.

$$80-\left(3\sqrt{7}\right)^{2}$$

Expand \left(3\sqrt{7}\right)^{2}.

$$80-3^{2}\left(\sqrt{7}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$80-9\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$80-9\times 7$$

Multiply 9 and 7 to get 63.

$$80-63$$

Subtract 63 from 80 to get 17.

$$17$$

Factor

$$17$$