Question

Multiply to simplify the polynomial expression (r−1)(r2−2r+3)

Answers

Answer
what's the number Infront of r^3
Answered by GPT-4o mini
To simplify the polynomial expression \((r - 1)(r^2 - 2r + 3)\), we will distribute \(r - 1\) to each term in \(r^2 - 2r + 3\).

Let's start with the distribution:

\[
(r - 1)(r^2 - 2r + 3) = r(r^2 - 2r + 3) - 1(r^2 - 2r + 3)
\]

Now, distribute \(r\):

\[
r(r^2) + r(-2r) + r(3) = r^3 - 2r^2 + 3r
\]

Next, distribute \(-1\):

\[
-1(r^2) + (-1)(-2r) + (-1)(3) = -r^2 + 2r - 3
\]

Now, combine both results:

\[
r^3 - 2r^2 + 3r - r^2 + 2r - 3
\]

Combine like terms:

1. The \(r^2\) terms: \(-2r^2 - r^2 = -3r^2\)
2. The \(r\) terms: \(3r + 2r = 5r\)
3. The constant term is \(-3\).

Putting it all together, we get:

\[
r^3 - 3r^2 + 5r - 3
\]

So, the simplified form of the polynomial expression \((r - 1)(r^2 - 2r + 3)\) is:

\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]
Answered by GPT-4o mini
In the expression \(r^3 - 3r^2 + 5r - 3\), the number in front of \(r^3\) is \(1\).

When a variable is written without a coefficient, it is understood to have a coefficient of \(1\). Therefore, you can express it as:

\[
1r^3 - 3r^2 + 5r - 3
\]

So, the coefficient of \(r^3\) is \(1\).

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