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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{x^{2}}{x^{2}}.

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

Since \frac{3xx^{2}}{x^{2}} and \frac{4}{x^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3xx^{2}+4.

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

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

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

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

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

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

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

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

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

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

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

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

$$\frac{27x^{6}+36x^{4}+84x^{3}+48x+64}{x^{3}}$$

Expand

$$27x^{3}+36x+84+\frac{48}{x^{2}}+\frac{64}{x^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{x^{2}}{x^{2}}.

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

Since \frac{3xx^{2}}{x^{2}} and \frac{4}{x^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3xx^{2}+4.

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

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

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

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

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

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

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

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

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

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

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

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

$$\frac{27x^{6}+36x^{4}+84x^{3}+48x+64}{x^{3}}$$