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

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

Evaluate

$$37$$

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}.

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

Calculate 7 to the power of 2 and get 49.

$$49-\left(2\sqrt{3}\right)^{2}$$

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

$$49-2^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$49-4\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$49-4\times 3$$

Multiply 4 and 3 to get 12.

$$49-12$$

Subtract 12 from 49 to get 37.

$$37$$

Factor

$$37$$