expand the expression to a polynomial in standard form:
$(4x + 5)(x^2 - 2x + 5)$

Question

Accepted Answer

# Explanation:
## Step1: Use the distributive property (FOIL for binomial and trinomial)
Multiply each term in the first polynomial by each term in the second polynomial:
$$
\begin{align*}
&(4x + 5)(x^2 - 2x + 5)\
=& 4x \cdot x^2 + 4x \cdot (-2x) + 4x \cdot 5 + 5 \cdot x^2 + 5 \cdot (-2x) + 5 \cdot 5\
\end{align*}
$$
## Step2: Simplify each term
Calculate each product:
$$
\begin{align*}
&4x^3 - 8x^2 + 20x + 5x^2 - 10x + 25\
\end{align*}
$$
## Step3: Combine like terms
Combine the $x^2$ terms and the $x$ terms:
$$
\begin{align*}
&4x^3 + (-8x^2 + 5x^2) + (20x - 10x) + 25\
=& 4x^3 - 3x^2 + 10x + 25\
\end{align*}
$$
# Answer:
$4x^3 - 3x^2 + 10x + 25$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the distributive property (FOIL for binomial and trinomial)

Step2: Simplify each term

Step3: Combine like terms

Answer: