Question

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

Answer 1

do this again

Answer 2

can u do this only with the numbers

Answer 3

To simplify the expression \((r - 1)(r^2 - 2r + 3)\), we'll use the distributive property (also known as the FOIL method for binomials).

Step 1: Distribute \(r\) from the first polynomial to each term in the second polynomial:
\[
r(r^2) + r(-2r) + r(3) = r^3 - 2r^2 + 3r
\]

Step 2: Distribute \(-1\) from the first polynomial to each term in the second polynomial:
\[
-1(r^2) + (-1)(-2r) + (-1)(3) = -r^2 + 2r - 3
\]

Step 3: Now combine all the terms together:
\[
r^3 - 2r^2 + 3r - r^2 + 2r - 3
\]

Step 4: Combine like terms:
\[
r^3 + (-2r^2 - r^2) + (3r + 2r) - 3 = r^3 - 3r^2 + 5r - 3
\]

Thus, the simplified form of the polynomial expression \((r - 1)(r^2 - 2r + 3)\) is:
\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]

Answer 4

Sure! Let's simplify the expression \((r - 1)(r^2 - 2r + 3)\) step by step.

### Step 1: Distribute \(r\) from the first polynomial to each term in the second polynomial.
\[
r(r^2) + r(-2r) + r(3) = r^3 - 2r^2 + 3r
\]

### Step 2: Distribute \(-1\) from the first polynomial to each term in the second polynomial.
\[
-1(r^2) + (-1)(-2r) + (-1)(3) = -r^2 + 2r - 3
\]

### Step 3: Combine all the terms together:
Now we put together the results from Step 1 and Step 2:
\[
r^3 - 2r^2 + 3r - r^2 + 2r - 3
\]

### Step 4: Combine like terms:
Combine the like terms:
- The \(r^2\) terms: \(-2r^2 - r^2 = -3r^2\)
- The \(r\) terms: \(3r + 2r = 5r\)

Putting it all together, we get:
\[
r^3 - 3r^2 + 5r - 3
\]

So, the simplified expression for \((r - 1)(r^2 - 2r + 3)\) is:
\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]

Answer 5

Sure! Let's simplify the expression \((r - 1)(r^2 - 2r + 3)\) using only the coefficients and constants without detailing the letters.

### Step 1: Distribute the first term
First, distribute \(r\):
- \(r \cdot 1 = r\)
- \(r \cdot (-2) = -2r\)
- \(r \cdot 3 = 3r\)

Adding these gives:
\[
1r - 2r + 3r
\]

### Step 2: Distribute the second term
Now, distribute \(-1\):
- \(-1 \cdot 1 = -1\)
- \(-1 \cdot (-2) = +2\)
- \(-1 \cdot 3 = -3\)

Adding these gives:
\[
-1 + 2 - 3
\]

### Step 3: Combine both results
Now combine all the terms together:
- Terms from distributing \(r\): \(r - 2r + 3r\) simplifies to \(2r\)
- Terms from distributing \(-1\): \(-1 + 2 - 3\) simplifies to \(-2\)

### Final Result:
So we have:
\[
1r + 0r - 2 \Rightarrow r^3 - 3r^2 + 5r - 3
\]

Thus, the simplified expression is:
\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]

I realize my explanation may still sound complex. Here is a truly numerical form:

### Direct Approach with Numerical Representation:
1. From \((1)(1) = 1\)
2. From \((r)(-2) = -2\)
3. From \((r)(3) = 3\)
4. From \((-1)(1) = -1\)
5. From \((-1)(-2) = 2\)
6. From \((-1)(3) = -3\)

Finally, combine:
- Coefficient of \(r^2\): \(-2 - 1 = -3\)
- Coefficient of \(r\): \(3 + 2 = 5\)

The constant term:
- Total = \(-1 + 2 - 3 = -2\)

Thus the final form stays:
\[
r^3 - 3r^2 + 5r - 2
\]
Which was a direct accounting resulted in maintaining the logical terms and please consider rectifying the distribution conditions or mentions. Let me know if you have another numerical focus or format inquiry!