Solve g(t)=(3+5/t^3)(3t^2+2t+5)

$$g ( t ) = ( 3 + \frac { 5 } { t ^ { 3 } } ) ( 3 t ^ { 2 } + 2 t + 5 )$$

Evaluate

$$\frac{\left(3t^{2}+2t+5\right)\left(3t^{3}+5\right)}{t^{3}}$$

Short Solution Steps

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

$$\left(\frac{3t^{3}}{t^{3}}+\frac{5}{t^{3}}\right)\left(3t^{2}+2t+5\right)$$

Since \frac{3t^{3}}{t^{3}} and \frac{5}{t^{3}} have the same denominator, add them by adding their numerators.

$$\frac{3t^{3}+5}{t^{3}}\left(3t^{2}+2t+5\right)$$

Express \frac{3t^{3}+5}{t^{3}}\left(3t^{2}+2t+5\right) as a single fraction.

$$\frac{\left(3t^{3}+5\right)\left(3t^{2}+2t+5\right)}{t^{3}}$$

Use the distributive property to multiply 3t^{3}+5 by 3t^{2}+2t+5.

$$\frac{9t^{5}+6t^{4}+15t^{3}+15t^{2}+10t+25}{t^{3}}$$

Expand

$$9t^{2}+6t+15+\frac{15}{t}+\frac{10}{t^{2}}+\frac{25}{t^{3}}$$

Short Solution Steps

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

$$\left(\frac{3t^{3}}{t^{3}}+\frac{5}{t^{3}}\right)\left(3t^{2}+2t+5\right)$$

Since \frac{3t^{3}}{t^{3}} and \frac{5}{t^{3}} have the same denominator, add them by adding their numerators.

$$\frac{3t^{3}+5}{t^{3}}\left(3t^{2}+2t+5\right)$$

Express \frac{3t^{3}+5}{t^{3}}\left(3t^{2}+2t+5\right) as a single fraction.

$$\frac{\left(3t^{3}+5\right)\left(3t^{2}+2t+5\right)}{t^{3}}$$

Use the distributive property to multiply 3t^{3}+5 by 3t^{2}+2t+5.

$$\frac{9t^{5}+6t^{4}+15t^{3}+15t^{2}+10t+25}{t^{3}}$$