Solve (2sqrt{7}-3sqrt{2})(2sqrt{7}+3sqrt{2})=

$$( 2 \sqrt { 7 } - 3 \sqrt { 2 } ) ( 2 \sqrt { 7 } + 3 \sqrt { 2 } ) =$$

Evaluate

$$10$$

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{7} is 7.

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

Multiply 4 and 7 to get 28.

$$28-\left(3\sqrt{2}\right)^{2}$$

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

$$28-3^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$28-9\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$28-9\times 2$$

Multiply 9 and 2 to get 18.

$$28-18$$

Subtract 18 from 28 to get 10.

$$10$$

Factor

$$2\times 5$$