Solve (x^2+2sqrt{3}x)(x^2-2sqrt{3}x)

$$( x ^ { 2 } + 2 \sqrt { 3 } x ) ( x ^ { 2 } - 2 \sqrt { 3 } x )$$

Evaluate

$$x^{2}\left(x^{2}-12\right)$$

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}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{3} is 3.

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

Multiply 4 and 3 to get 12.

$$x^{4}-12x^{2}$$

Factor

$$x^{2}\left(x^{2}-12\right)$$