 
Expand 2x³+7x²+x-1 I the power of( x-2)

To expand \((2x^3 + 7x^2 + x - 1)(x - 2)\), we distribute each term of \((2x^3 + 7x^2 + x - 1)\) by \((x - 2)\). Here's how it works step by step:

### Step 1: Distribute each term
\[
(2x^3 + 7x^2 + x - 1)(x - 2)
\]

First, distribute the \(x\) from \((x - 2)\) to each term in \((2x^3 + 7x^2 + x - 1)\):
\[
x(2x^3 + 7x^2 + x - 1) = 2x^4 + 7x^3 + x^2 - x
\]

Now, distribute the \(-2\) to each term in \((2x^3 + 7x^2 + x - 1)\):
\[
-2(2x^3 + 7x^2 + x - 1) = -4x^3 - 14x^2 - 2x + 2
\]

### Step 2: Add the distributed terms
Now, add the two parts together:
\[
(2x^4 + 7x^3 + x^2 - x) + (-4x^3 - 14x^2 - 2x + 2)
\]

Combine like terms:
\[
2x^4 + (7x^3 - 4x^3) + (x^2 - 14x^2) + (-x - 2x) + 2
\]
\[
= 2x^4 + 3x^3 - 13x^2 - 3x + 2
\]

### Final Answer:
\[
2x^4 + 3x^3 - 13x^2 - 3x + 2
\]

Would you like more details on any specific step?

Here are 5 related questions:
1. How would the result change if you expanded \((2x^3 + 7x^2 + x - 1)(x + 2)\)?
2. What would the expansion of \((x^2 + 3x - 5)(x - 2)\) look like?
3. Can you factor the polynomial \(2x^4 + 3x^3 - 13x^2 - 3x + 2\)?
4. How would the degree of the polynomial change if you multiplied by \((x^2 - 2x + 1)\)?
5. What are the roots of \(2x^4 + 3x^3 - 13x^2 - 3x + 2 = 0\)?

**Tip:** Always organize your terms carefully when distributing and combining like terms to avoid mistakes.

Expand 2x³+7x²+x-1 in the power of (x-2)

Learn how to expand the polynomial expression (2x³ + 7x² + x - 1)(x - 2) using the distributive property. This step-by-step solution demonstrates key algebraic concepts, including polynomial multiplication and combining like terms. Suitable for students in Grades 9-10.

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