Question

Identify the first and last terms of the simplified expression 4x^2(5x^3+4x+1)-9x^5+3x^2+4

Answer 1

To simplify the expression \(4x^2(5x^3 + 4x + 1) - 9x^5 + 3x^2 + 4\), we will first distribute \(4x^2\) across the terms inside the parentheses.

Starting with the distribution:

\[
4x^2 \cdot 5x^3 = 20x^5,
\]
\[
4x^2 \cdot 4x = 16x^3,
\]
\[
4x^2 \cdot 1 = 4x^2.
\]

Now we can rewrite the expression as:

\[
20x^5 + 16x^3 + 4x^2 - 9x^5 + 3x^2 + 4.
\]

Next, we will combine the like terms. First, we combine the \(x^5\) terms:

\[
20x^5 - 9x^5 = 11x^5.
\]

Now we combine the \(x^3\) terms:

\[
16x^3.
\]

Next, we combine the \(x^2\) terms:

\[
4x^2 + 3x^2 = 7x^2.
\]

Finally, the constant term remains:

\[
4.
\]

Putting it all together, we have:

\[
11x^5 + 16x^3 + 7x^2 + 4.
\]

Now we can identify the first and last terms of the simplified expression:

- **First term**: \(11x^5\)
- **Last term**: \(4\)

Thus, the first term is \(11x^5\) and the last term is \(4\).