https://file.aiquickdraw.com/mathbot/file/1726516928217ybatu1ce.jpg

The expression provided in the image is:

\[
(2x + 1)^2 + (x - 1)^2 - 2(7x - 1) = 
\]

Let's simplify and solve it step by step.

### Step 1: Expand the squares
First, expand the square terms:

\[
(2x + 1)^2 = (2x)^2 + 2(2x)(1) + (1)^2 = 4x^2 + 4x + 1
\]

\[
(x - 1)^2 = (x)^2 - 2(x)(1) + (1)^2 = x^2 - 2x + 1
\]

### Step 2: Expand the linear term
Next, expand the term involving the multiplication by 2:

\[
2(7x - 1) = 2 \times 7x - 2 \times 1 = 14x - 2
\]

### Step 3: Combine all terms
Now, combine everything together:

\[
4x^2 + 4x + 1 + x^2 - 2x + 1 - (14x - 2)
\]

### Step 4: Simplify
Now, let's combine like terms:

- \( 4x^2 + x^2 = 5x^2 \)
- \( 4x - 2x - 14x = -12x \)
- \( 1 + 1 + 2 = 4 \)

So, the expression simplifies to:

\[
5x^2 - 12x + 4
\]

Thus, the simplified form of the given expression is:

\[
5x^2 - 12x + 4
\]

Would you like any additional details or clarifications? Here are some related questions you can explore:

1. What happens if we solve \( 5x^2 - 12x + 4 = 0 \)?
2. How do you factor quadratic expressions like \( 5x^2 - 12x + 4 \)?
3. What are the possible real or complex roots of the simplified expression?
4. How does the discriminant help in solving quadratic equations?
5. How can you apply this process to other similar problems?

**Tip:** Always double-check for sign changes when expanding and combining terms to avoid common mistakes.

Learn how to simplify the expression (2x + 1)^2 + (x - 1)^2 - 2(7x - 1) with a detailed step-by-step solution. This problem involves key algebraic concepts such as polynomial expansion and the quadratic formula. Suitable for students in Grades 9-11.

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