Q. 269 - Intermediate Algebra

Question

 In the following exercises , simplify the equation $\left(6k\hspace{0.17em}-\hspace{0.17em}1\right)\left(k^2\hspace{0.17em}+\hspace{0.17em}2k\hspace{0.17em}-\hspace{0.17em}4\right)$.

Step-by-Step Solution

Answer

The simplified expression is $6k^3+11k^2-26k+4$.

Step 1. Given Information.

The expression is $\left(6k\hspace{0.17em}-\hspace{0.17em}1\right)\left(k^2\hspace{0.17em}+\hspace{0.17em}2k\hspace{0.17em}-\hspace{0.17em}4\right)$.

Step 2. Simplify given equation.

Simplifying $\left(6k\hspace{0.17em}-\hspace{0.17em}1\right)\left(k^2\hspace{0.17em}+\hspace{0.17em}2k\hspace{0.17em}-\hspace{0.17em}4\right)$

Distributing parentheses:-

$$\begin{gathered} \left(6k-1\right)\left(k^2+2k-4\right)=6k{k}^2+6k·\hspace{0.17em}2k+6k\left(-4\right)-1·\hspace{0.17em}{k}^2-1·\hspace{0.17em}2k-1·\left(-4\right) \\ 6k{k}^2+6k·\hspace{0.17em}2k+6k\left(-4\right)-1·\hspace{0.17em}{k}^2-1·\hspace{0.17em}2k-1·\left(-4\right)=6k^3+11k^2-26k+4 \end{gathered}$$