Let's solve the expression \((-2x + 1)^2 - 4\).

### Step 1: Expand the square
\[
(-2x + 1)^2 = (-2x + 1)(-2x + 1)
\]
Applying the distributive property (FOIL):
\[
= (-2x)(-2x) + (-2x)(1) + (1)(-2x) + (1)(1)
\]
\[
= 4x^2 - 2x - 2x + 1
\]
\[
= 4x^2 - 4x + 1
\]

### Step 2: Subtract 4
Now subtract 4 from the expanded expression:
\[
4x^2 - 4x + 1 - 4
\]
\[
= 4x^2 - 4x - 3
\]

So, the simplified expression is:
\[
4x^2 - 4x - 3
\]

Would you like further explanation on any step?

Here are 5 related questions for practice:
1. Expand \((3x - 2)^2\).
2. Simplify \((x - 5)^2 - 9\).
3. Solve \((2x + 3)^2 - 5 = 0\).
4. Factor \(4x^2 - 4x - 3\).
5. What is the vertex form of the quadratic equation \(4x^2 - 4x - 3\)?

**Tip:** When expanding binomials, always apply the distributive property (FOIL) to ensure accuracy in each term.

Solve and simplify the quadratic expression (-2x + 1)^2 - 4. This solution demonstrates the expansion of binomials using the FOIL method and the distributive property, resulting in the simplified form 4x^2 - 4x - 3. Suitable for students in Grades 8-10.

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