Solve (2x+1/x)(4x^2+1/x^2-2)

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

Evaluate

$$8x^{3}+\frac{1}{x^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{x}{x}.

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

Since \frac{2xx}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2xx+1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x^{2}-2 times \frac{x^{2}}{x^{2}}.

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

Since \frac{\left(4x^{2}-2\right)x^{2}}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(4x^{2}-2\right)x^{2}+1.

$$\frac{2x^{2}+1}{x}\times \frac{4x^{4}-2x^{2}+1}{x^{2}}$$

Multiply \frac{2x^{2}+1}{x} times \frac{4x^{4}-2x^{2}+1}{x^{2}} by multiplying numerator times numerator and denominator times denominator.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(2x^{2}+1\right)\left(4x^{4}-2x^{2}+1\right)}{x^{3}}$$

Use the distributive property to multiply 2x^{2}+1 by 4x^{4}-2x^{2}+1 and combine like terms.

$$\frac{8x^{6}+1}{x^{3}}$$

Expand

$$8x^{3}+\frac{1}{x^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{x}{x}.

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

Since \frac{2xx}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2xx+1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x^{2}-2 times \frac{x^{2}}{x^{2}}.

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

Since \frac{\left(4x^{2}-2\right)x^{2}}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(4x^{2}-2\right)x^{2}+1.

$$\frac{2x^{2}+1}{x}\times \frac{4x^{4}-2x^{2}+1}{x^{2}}$$

Multiply \frac{2x^{2}+1}{x} times \frac{4x^{4}-2x^{2}+1}{x^{2}} by multiplying numerator times numerator and denominator times denominator.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(2x^{2}+1\right)\left(4x^{4}-2x^{2}+1\right)}{x^{3}}$$

Use the distributive property to multiply 2x^{2}+1 by 4x^{4}-2x^{2}+1 and combine like terms.

$$\frac{8x^{6}+1}{x^{3}}$$