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

Answer 1

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:

\[ \boxed{r^3 - 3r^2 + 5r - 3} \]

Answer 2

what's the number Infront of r^3

Answer 3

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 \(1\).