To simplify the expression \(-3(x+h)^2 - 7\), we'll expand it step by step.

### Step 1: Expand the squared term
\[
(x + h)^2 = (x + h)(x + h)
\]
Using the distributive property (FOIL method):
\[
(x + h)(x + h) = x^2 + 2xh + h^2
\]

### Step 2: Multiply by -3
Now, multiply the expanded form by \(-3\):
\[
-3(x^2 + 2xh + h^2) = -3x^2 - 6xh - 3h^2
\]

### Step 3: Subtract 7
Finally, subtract 7 from the entire expression:
\[
-3x^2 - 6xh - 3h^2 - 7
\]

So, the simplified form of the expression is:
\[
-3x^2 - 6xh - 3h^2 - 7
\]

Would you like more details, or do you have any questions?

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Here are 5 related questions:

1. What happens if you set \(h = 0\) in this expression?
2. How would you factor the quadratic expression \(-3x^2 - 6xh - 3h^2\)?
3. Can you identify the vertex of the quadratic function in terms of \(x\) and \(h\)?
4. How would you graph this expression in terms of \(x\) and \(h\)?
5. What is the effect of changing the coefficient \(-3\) to another value, like \(4\)?

**Tip:** When expanding binomials, always apply the distributive property carefully to avoid missing terms!

Learn how to simplify the expression -3(x+h)^2 - 7 step by step. Understand the FOIL method and distributive property used in expanding binomials. Suitable for Grades 10-12.

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