Question

find $(-2r - 3)(5r - 1)(r + 4)$.

Explanation:

Step1: Multiply the first two binomials

First, multiply \((-2r - 3)\) and \((5r - 1)\) using the distributive property (FOIL method):
\[

$$\begin{align*} (-2r - 3)(5r - 1)&=-2r\times5r+(-2r)\times(-1)+(-3)\times5r+(-3)\times(-1)\\ &=-10r^{2}+2r - 15r + 3\\ &=-10r^{2}-13r + 3 \end{align*}$$

\]

Step2: Multiply the result by the third binomial

Now, multiply \((-10r^{2}-13r + 3)\) by \((r + 4)\):
\[

$$\begin{align*} (-10r^{2}-13r + 3)(r + 4)&=-10r^{2}\times r+(-10r^{2})\times4+(-13r)\times r+(-13r)\times4+3\times r+3\times4\\ &=-10r^{3}-40r^{2}-13r^{2}-52r + 3r + 12\\ &=-10r^{3}+(-40r^{2}-13r^{2})+(-52r + 3r)+12\\ &=-10r^{3}-53r^{2}-49r + 12 \end{align*}$$

\]

Answer:

\(-10r^{3}-53r^{2}-49r + 12\)