VIPSolutionsgive answer in 2 step with explanation at the end of each step and final answer at the end:2) y= (a2) 2x41) |
Question:
give answer in 2 step with explanation at the end of each step and final answer at the end:
2) y= (a2) 2x41) |
This is AI generated Response.
Asked by: Pagal
Created at: 2025-08-06 21:45:34
Asked by: Pagal
Created at: 2025-08-06 21:45:34
Final Answer:
Rendered
Raw Text
Did you like this answer?
Sure! The equation given is:
\[ y = (x^2 + 2)(x^2 - 2x + 1) \]
Let's expand and simplify it in **2 steps**, with explanations:
---
### **Step 1: Expand \( (x^2 - 2x + 1) \)**
Notice that \( x^2 - 2x + 1 \) can be factored as \( (x - 1)^2 \).
**Explanation:**
Recognizing perfect square trinomials helps to make multiplication easier.
So the equation becomes:
\[
y = (x^2 + 2)\left[(x - 1)^2\right]
\]
---
### **Step 2: Expand the product \((x^2 + 2)(x - 1)^2\)**
First, expand \( (x - 1)^2 = x^2 - 2x + 1 \).
Now, distribute \( (x^2 + 2) \) to each term in \( (x^2 - 2x + 1) \):
\[
y = (x^2 + 2)(x^2 - 2x + 1)
\]
\[
= x^2(x^2 - 2x + 1) + 2(x^2 - 2x + 1)
\]
\[
= (x^4 - 2x^3 + x^2) + (2x^2 - 4x + 2)
\]
\[
= x^4 - 2x^3 + x^2 + 2x^2 - 4x + 2
\]
\[
= x^4 - 2x^3 + 3x^2 - 4x + 2
\]
**Explanation:**
We expanded the expression and combined like terms.
---
## **Final Answer:**
\[
\boxed{y = x^4 - 2x^3 + 3x^2 - 4x + 2}
\]
📢 Instructions:
- Ask anything relatd to above question only.
- For new Question goto :