Question

Use the following model find the algebraic expression it represents A 2 n + 4 B n + 4 C 4 n + 2 D 2 n + 2 expression 1 n +1 + 1

Answer 1

To determine the algebraic expression represented by the model you provided, we can begin by organizing the terms clearly based on the variables and coefficients.

The original expression seems to be:

\(A 2n + 4 B n + 4 C 4n + 2 D 2n + 2 \text{ expression } 1n + 1 + 1\)

This appears to include multiple terms, and it looks like it might be best interpreted as a sum of several polynomial expressions involving the variable \(n\).

Let's break it down:

- **Terms with A**: \(2An\)
- **Terms with B**: \(4Bn\)
- **Terms with C**: \(4C(4n) = 16Cn\)
- **Terms with D**: \(2D(2n) = 4Dn\)
- A constant term, possibly \(2\) from \(2D\) or others.

Then we see the last part which has \( 1n + 1 + 1\) that can be interpreted as simply:

\(n + 2\)

Now, combining all these together, we write the expression as:

\[
(2A + 4B + 16C + 4D + 1)n + (2 + 1)
\]

Now simplifying further:

The coefficient of \(n\) becomes \((2A + 4B + 16C + 4D + 1)\), and the constant term becomes \(3\).

Thus, the entire framework can be expressed as:

\[
(2A + 4B + 16C + 4D + 1)n + 3
\]

This is the algebraic expression represented by the original input terms, where \(A\), \(B\), \(C\), and \(D\) can take any real values and \(n\) is treated as a variable.

If you have specific values for \(A\), \(B\), \(C\), and \(D\), they can be substituted to get a numerical polynomial.