Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Multiply to simplify the polynomial expression (r−1)(r2−2r+3).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:
\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]
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 \(1\).
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 \(1\).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.