Question

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

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:

\(4x^3 - 3x^2 + 10x + 25\)