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