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

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

Evaluate

$$3$$

Solution Steps

Consider \left(\sqrt{3}-2\sqrt{3}\right)\left(\sqrt{3}+2\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

The square of \sqrt{3} is 3.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{3} is 3.

$$\frac{3-4\times 3}{-3}$$

Multiply 4 and 3 to get 12.

$$\frac{3-12}{-3}$$

Subtract 12 from 3 to get -9.

$$\frac{-9}{-3}$$

Divide -9 by -3 to get 3.

$$3$$

Factor

$$3$$