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.