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

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

Evaluate

$$19$$

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{7} is 7.

$$4\times 7-3^{2}$$

Multiply 4 and 7 to get 28.

$$28-3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$28-9$$

Subtract 9 from 28 to get 19.

$$19$$

Factor

$$19$$