Solve (x^3+1/x^3)(x^3-1/x^3)=

$$( x ^ { 3 } + \frac { 1 } { x ^ { 3 } } ) ( x ^ { 3 } - \frac { 1 } { x ^ { 3 } } ) =$$

Evaluate

$$\frac{\left(x^{4}-1\right)\left(\left(x^{4}+1\right)^{2}-x^{4}\right)}{x^{6}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3} times \frac{x^{3}}{x^{3}}.

$$\left(\frac{x^{3}x^{3}}{x^{3}}+\frac{1}{x^{3}}\right)\left(x^{3}-\frac{1}{x^{3}}\right)$$

Since \frac{x^{3}x^{3}}{x^{3}} and \frac{1}{x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{x^{3}x^{3}+1}{x^{3}}\left(x^{3}-\frac{1}{x^{3}}\right)$$

Do the multiplications in x^{3}x^{3}+1.

$$\frac{x^{6}+1}{x^{3}}\left(x^{3}-\frac{1}{x^{3}}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3} times \frac{x^{3}}{x^{3}}.

$$\frac{x^{6}+1}{x^{3}}\left(\frac{x^{3}x^{3}}{x^{3}}-\frac{1}{x^{3}}\right)$$

Since \frac{x^{3}x^{3}}{x^{3}} and \frac{1}{x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{6}+1}{x^{3}}\times \frac{x^{3}x^{3}-1}{x^{3}}$$

Do the multiplications in x^{3}x^{3}-1.

$$\frac{x^{6}+1}{x^{3}}\times \frac{x^{6}-1}{x^{3}}$$

Multiply \frac{x^{6}+1}{x^{3}} times \frac{x^{6}-1}{x^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{6}+1\right)\left(x^{6}-1\right)}{x^{3}x^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{\left(x^{6}+1\right)\left(x^{6}-1\right)}{x^{6}}$$

Consider \left(x^{6}+1\right)\left(x^{6}-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}. Square 1.

$$\frac{\left(x^{6}\right)^{2}-1}{x^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{x^{12}-1}{x^{6}}$$

Expand

$$x^{6}-\frac{1}{x^{6}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3} times \frac{x^{3}}{x^{3}}.

$$\left(\frac{x^{3}x^{3}}{x^{3}}+\frac{1}{x^{3}}\right)\left(x^{3}-\frac{1}{x^{3}}\right)$$

Since \frac{x^{3}x^{3}}{x^{3}} and \frac{1}{x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{x^{3}x^{3}+1}{x^{3}}\left(x^{3}-\frac{1}{x^{3}}\right)$$

Do the multiplications in x^{3}x^{3}+1.

$$\frac{x^{6}+1}{x^{3}}\left(x^{3}-\frac{1}{x^{3}}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3} times \frac{x^{3}}{x^{3}}.

$$\frac{x^{6}+1}{x^{3}}\left(\frac{x^{3}x^{3}}{x^{3}}-\frac{1}{x^{3}}\right)$$

Since \frac{x^{3}x^{3}}{x^{3}} and \frac{1}{x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{6}+1}{x^{3}}\times \frac{x^{3}x^{3}-1}{x^{3}}$$

Do the multiplications in x^{3}x^{3}-1.

$$\frac{x^{6}+1}{x^{3}}\times \frac{x^{6}-1}{x^{3}}$$

Multiply \frac{x^{6}+1}{x^{3}} times \frac{x^{6}-1}{x^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{6}+1\right)\left(x^{6}-1\right)}{x^{3}x^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{\left(x^{6}+1\right)\left(x^{6}-1\right)}{x^{6}}$$

Consider \left(x^{6}+1\right)\left(x^{6}-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}. Square 1.

$$\frac{\left(x^{6}\right)^{2}-1}{x^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{x^{12}-1}{x^{6}}$$