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

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

Evaluate

$$1$$

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}.

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

Calculate 7 to the power of 2 and get 49.

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

Expand \left(4\sqrt{3}\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$49-16\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$49-16\times 3$$

Multiply 16 and 3 to get 48.

$$49-48$$

Subtract 48 from 49 to get 1.

$$1$$

Factor

$$1$$