Questions: 1/4 x^3 - x^2 - 1/6 x^2 + 3/8 x^3 + 1/16 x^3 1/4 x^3 - x^2 - 1/6 x^2 + 3/8 x^3 + 1/16 x^3 =

Solution Steps

To collect like terms, we need to combine the coefficients of the same powers of $x$. In this case, we have terms with $x^3$ and $x^2$. We will sum the coefficients of $x^3$ and $x^2$ separately.

We start with the terms involving $x^3$: $$\frac{1}{4} x^3 + \frac{3}{8} x^3 + \frac{1}{16} x^3$$ Calculating the coefficients: $$\frac{1}{4} + \frac{3}{8} + \frac{1}{16} = \frac{11}{16}$$ Thus, the combined term for $x^3$ is: $$\frac{11}{16} x^3$$

Next, we combine the terms involving $x^2$: $$-x^2 - \frac{1}{6} x^2$$ Calculating the coefficients: $$-1 - \frac{1}{6} = -\frac{6}{6} - \frac{1}{6} = -\frac{7}{6}$$ Thus, the combined term for $x^2$ is: $$-\frac{7}{6} x^2$$

Combining both results, we have: $$\frac{11}{16} x^3 - \frac{7}{6} x^2$$

Final Answer