Question

What is the error made when subtracting these two polynomials
(2x^3-7x^2+4x)-(9x-5x^3+9x^2)
Step 1: 2x^3-7x^2+4x-9x-5x^3+9x^2
Step 2: 2x^3-5x^3-7x^2+9x^2+4x-9x
Step 3: -3x^3+2x^2-5x
Final answer: -3x^3+2x^2-5x

Answer 1

In which step was there an error

Answer 2

why am I supposed to add 2x^3 and 5x^3 instead of subtract?

Answer 3

Let's go through the polynomial subtraction step by step to identify any errors.

1. Start with the original expression:
\[
(2x^3 - 7x^2 + 4x) - (9x - 5x^3 + 9x^2)
\]
This can be rewritten as:
\[
2x^3 - 7x^2 + 4x - 9x + 5x^3 - 9x^2
\]

2. Combine like terms (in the order you did, your work is generally correct):
\[
(2x^3 + 5x^3) + (-7x^2 - 9x^2) + (4x - 9x)
\]

3. Calculate each part:
- For the \(x^3\) terms: \(2x^3 + 5x^3 = 7x^3\)
- For the \(x^2\) terms: \(-7x^2 - 9x^2 = -16x^2\)
- For the \(x\) terms: \(4x - 9x = -5x\)

4. Therefore, combining all the results yields:
\[
7x^3 - 16x^2 - 5x
\]

Thus, the corrected final answer should be:
\[
7x^3 - 16x^2 - 5x
\]

The error in your solution was in the combination of the \(x^3\) and \(x^2\) terms. You subtracted instead of adding the coefficients correctly.

Answer 4

Let's break down each step of your polynomial subtraction to pinpoint where the error occurred:

1. **Original Step**:
\[
(2x^3 - 7x^2 + 4x) - (9x - 5x^3 + 9x^2)
\]
You correctly rewrite this as:
\[
2x^3 - 7x^2 + 4x - 9x + 5x^3 - 9x^2
\]

2. **Step 1**: You arranged the terms:
\[
2x^3 - 7x^2 + 4x - 9x - 5x^3 + 9x^2
\]
This step appears correct.

3. **Step 2**: You combined like terms:
\[
2x^3 - 5x^3 - 7x^2 + 9x^2 + 4x - 9x
\]
The arrangement of terms looks fine here as well.

4. **Step 3**: Then combined them:
\[
-3x^3 + 2x^2 - 5x
\]
Here's where the error occurred:
- For the \(x^3\) terms:
- You should have \(2x^3 + 5x^3 = 7x^3\), but instead you wrote \(-3x^3\).
- For the \(x^2\) terms:
- You should have \(-7x^2 - 9x^2 = -16x^2\), but instead you wrote \(2x^2\).

5. **Final answer**: Your answer of \(-3x^3 + 2x^2 - 5x\) is incorrect due to both mishaps in the combination of the \(x^3\) and \(x^2\) terms.

The correct final answer, after checking all the steps, should indeed be:
\[
7x^3 - 16x^2 - 5x
\]

In summary, the errors were in Step 3, specifically in the calculations of the coefficients of \(x^3\) and \(x^2\).

Answer 5

In the expression you provided, you are subtracting one polynomial from another. Let's clarify how to manage the signs when performing subtraction.

When you subtract a polynomial, you distribute the negative sign (or the minus sign) across all the terms of the polynomial being subtracted. This alters the signs of those terms. Here's a breakdown of this process:

### Original Expression
You started with:

\[
(2x^3 - 7x^2 + 4x) - (9x - 5x^3 + 9x^2)
\]

### Step 1: Distributing the Negative Sign
When you subtract the second polynomial, you distribute the negative sign through its terms:

\[
= 2x^3 - 7x^2 + 4x - 9x + 5x^3 - 9x^2
\]

As you can see, the term \(-5x^3\) comes from the original polynomial \( -( -5x^3)\) which becomes \(+5x^3\).

### Step 2: Combine Like Terms
Now, you combine like terms. Here’s how you combine them:

1. **Combine the \(x^3\) terms**:
- You have \(2x^3\) from the first polynomial and \(+5x^3\) from the second polynomial after distribution. So:
\[
2x^3 + 5x^3 = 7x^3
\]

2. **Combine the \(x^2\) terms**:
- You have \(-7x^2\) from the first polynomial and \(-9x^2\) from the second polynomial after distributing. Thus:
\[
-7x^2 - 9x^2 = -16x^2
\]

3. **Combine the \(x\) terms**:
- You have \(4x\) from the first polynomial and \(-9x\) from the second polynomial after distributing. Therefore:
\[
4x - 9x = -5x
\]

### Result
Combining these, you arrive at:
\[
7x^3 - 16x^2 - 5x
\]

### Conclusion
You were supposed to **add** \(2x^3\) and \(5x^3\) because when you distribute the negative sign, the term \(-5x^3\) becomes \(+5x^3\). When combining the coefficients of like terms, that leads you to **addition**, not subtraction for the \(x^3\) terms.

This is why understanding the distribution of the negative sign in polynomial subtraction is crucial for correctly combining the terms.