Solve (4sqrt{3}+1)(8*frac{sqrt{3}}{2}-1)

$$( 4 \sqrt { 3 } + 1 ) ( 8 \times \frac { \sqrt { 3 } } { 2 } - 1 )$$

Evaluate

$$47$$

Solution Steps

Cancel out 2, the greatest common factor in 8 and 2.

$$\left(4\sqrt{3}+1\right)\left(4\sqrt{3}-1\right)$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(4\sqrt{3}\right)^{2}-1^{2}$$

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

$$4^{2}\left(\sqrt{3}\right)^{2}-1^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{3}\right)^{2}-1^{2}$$

The square of \sqrt{3} is 3.

$$16\times 3-1^{2}$$

Multiply 16 and 3 to get 48.

$$48-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$48-1$$

Subtract 1 from 48 to get 47.

$$47$$

Factor

$$47$$