expand the expression to a polynomial in standard form:
$(x - 2)(3x + 1)(x + 1)(x + 4)$

Question

Accepted Answer

# Explanation:
## Step1: Multiply first two factors
Multiply $(x - 2)$ and $(3x + 1)$:
$$
\begin{align*}
(x - 2)(3x + 1)&=x(3x + 1)-2(3x + 1)\
&=3x^2+x - 6x - 2\
&=3x^2-5x - 2
\end{align*}
$$
## Step2: Multiply last two factors
Multiply $(x + 1)$ and $(x + 4)$:
$$
\begin{align*}
(x + 1)(x + 4)&=x(x + 4)+1(x + 4)\
&=x^2+4x+x + 4\
&=x^2+5x + 4
\end{align*}
$$
## Step3: Multiply the two results
Now multiply $(3x^2-5x - 2)$ and $(x^2+5x + 4)$:
$$
\begin{align*}
&(3x^2-5x - 2)(x^2+5x + 4)\
=&3x^2(x^2+5x + 4)-5x(x^2+5x + 4)-2(x^2+5x + 4)\
=&3x^4+15x^3+12x^2-5x^3-25x^2-20x-2x^2-10x - 8\
=&3x^4+(15x^3-5x^3)+(12x^2-25x^2-2x^2)+(-20x-10x)-8\
=&3x^4+10x^3-15x^2-30x - 8
\end{align*}
$$
# Answer:
$3x^4 + 10x^3 - 15x^2 - 30x - 8$

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QUESTION IMAGE

Question

Explanation:

Step1: Multiply first two factors

Step2: Multiply last two factors

Step3: Multiply the two results

Answer: