Multiply. \( \begin{array}{l}(c+f)\left(c^{2}-c f+f^{2}\right) \\ (c+f)\left(c^{2}-c f+f^{2}\right)=\square \\ (\text { Simplify your answer.) }\end{array} \)

To multiply \( (c+f)(c^2 - cf + f^2) \), we will use the distributive property (also known as the FOIL method for binomials). Let's start by distributing \( c \) over the trinomial: 1. \( c \cdot c^2 = c^3 \) 2. \( c \cdot (-cf) = -c^2f \) 3. \( c \cdot f^2 = cf^2 \) Next, we distribute \( f \) over the trinomial: 1. \( f \cdot c^2 = fc^2 \) 2. \( f \cdot (-cf) = -f^2c \) 3. \( f \cdot f^2 = f^3 \) Now, we combine all of these results: \[ c^3 - c^2f + cf^2 + fc^2 - f^2c + f^3 \] Notice that \( -c^2f + fc^2 \) and \( cf^2 - f^2c \) are like terms, so they combine to zero. Therefore, we can simplify the expression: \[ c^3 + f^3 \] Thus, the simplified answer is: \[ (c+f)(c^2 - cf + f^2) = c^3 + f^3 \]