Solve (3x+4/x)(9x^2-12+16/x^2)

$$( 3 x + \frac { 4 } { x } ) ( 9 x ^ { 2 } - 12 + \frac { 16 } { x ^ { 2 } } )$$

Evaluate

$$27x^{3}+\frac{64}{x^{3}}$$

Short Solution Steps

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

$$\left(\frac{3xx}{x}+\frac{4}{x}\right)\left(9x^{2}-12+\frac{16}{x^{2}}\right)$$

Since \frac{3xx}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.

$$\frac{3xx+4}{x}\left(9x^{2}-12+\frac{16}{x^{2}}\right)$$

Do the multiplications in 3xx+4.

$$\frac{3x^{2}+4}{x}\left(9x^{2}-12+\frac{16}{x^{2}}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9x^{2}-12 times \frac{x^{2}}{x^{2}}.

$$\frac{3x^{2}+4}{x}\left(\frac{\left(9x^{2}-12\right)x^{2}}{x^{2}}+\frac{16}{x^{2}}\right)$$

Since \frac{\left(9x^{2}-12\right)x^{2}}{x^{2}} and \frac{16}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3x^{2}+4}{x}\times \frac{\left(9x^{2}-12\right)x^{2}+16}{x^{2}}$$

Do the multiplications in \left(9x^{2}-12\right)x^{2}+16.

$$\frac{3x^{2}+4}{x}\times \frac{9x^{4}-12x^{2}+16}{x^{2}}$$

Multiply \frac{3x^{2}+4}{x} times \frac{9x^{4}-12x^{2}+16}{x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3x^{2}+4\right)\left(9x^{4}-12x^{2}+16\right)}{xx^{2}}$$

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

$$\frac{\left(3x^{2}+4\right)\left(9x^{4}-12x^{2}+16\right)}{x^{3}}$$

Use the distributive property to multiply 3x^{2}+4 by 9x^{4}-12x^{2}+16 and combine like terms.

$$\frac{27x^{6}+64}{x^{3}}$$

Expand

$$27x^{3}+\frac{64}{x^{3}}$$

Short Solution Steps

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

$$\left(\frac{3xx}{x}+\frac{4}{x}\right)\left(9x^{2}-12+\frac{16}{x^{2}}\right)$$

Since \frac{3xx}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.

$$\frac{3xx+4}{x}\left(9x^{2}-12+\frac{16}{x^{2}}\right)$$

Do the multiplications in 3xx+4.

$$\frac{3x^{2}+4}{x}\left(9x^{2}-12+\frac{16}{x^{2}}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9x^{2}-12 times \frac{x^{2}}{x^{2}}.

$$\frac{3x^{2}+4}{x}\left(\frac{\left(9x^{2}-12\right)x^{2}}{x^{2}}+\frac{16}{x^{2}}\right)$$

Since \frac{\left(9x^{2}-12\right)x^{2}}{x^{2}} and \frac{16}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3x^{2}+4}{x}\times \frac{\left(9x^{2}-12\right)x^{2}+16}{x^{2}}$$

Do the multiplications in \left(9x^{2}-12\right)x^{2}+16.

$$\frac{3x^{2}+4}{x}\times \frac{9x^{4}-12x^{2}+16}{x^{2}}$$

Multiply \frac{3x^{2}+4}{x} times \frac{9x^{4}-12x^{2}+16}{x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3x^{2}+4\right)\left(9x^{4}-12x^{2}+16\right)}{xx^{2}}$$

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

$$\frac{\left(3x^{2}+4\right)\left(9x^{4}-12x^{2}+16\right)}{x^{3}}$$

Use the distributive property to multiply 3x^{2}+4 by 9x^{4}-12x^{2}+16 and combine like terms.

$$\frac{27x^{6}+64}{x^{3}}$$