(x+6) 
2
 −(x−6) 
2
 +(x+4) 
2
 −(x−4) 
2
 −40x

To solve or simplify the given expression:

\[
(x+6)^2 - (x-6)^2 + (x+4)^2 - (x-4)^2 - 40x
\]

we'll expand each squared term and combine like terms to simplify the expression.

### Step 1: Expand the squared terms

1. \((x+6)^2 = x^2 + 12x + 36\)
2. \((x-6)^2 = x^2 - 12x + 36\)
3. \((x+4)^2 = x^2 + 8x + 16\)
4. \((x-4)^2 = x^2 - 8x + 16\)

### Step 2: Substitute and simplify

Now, substitute these expanded terms into the original expression:

\[
(x^2 + 12x + 36) - (x^2 - 12x + 36) + (x^2 + 8x + 16) - (x^2 - 8x + 16) - 40x
\]

### Step 3: Combine like terms

Simplify the expression:

\[
x^2 + 12x + 36 - x^2 + 12x - 36 + x^2 + 8x + 16 - x^2 + 8x - 16 - 40x
\]

Notice that the \(x^2\) terms cancel out:

\[
12x + 12x + 8x + 8x - 40x + 36 - 36 + 16 - 16
\]

Now, combine the \(x\) terms:

\[
(12x + 12x + 8x + 8x - 40x) = 0
\]

And combine the constant terms:

\[
36 - 36 + 16 - 16 = 0
\]

### Final Answer

The expression simplifies to:

\[
0
\]

So, the given expression simplifies to **0**.

---

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

Here are 5 related questions you might consider:
1. What happens when you simplify expressions with different powers of variables?
2. How do you apply the distributive property to simplify expressions?
3. What is the importance of combining like terms in algebra?
4. How do we solve quadratic equations by factoring?
5. What are the common algebraic identities useful in expanding squared binomials?

**Tip:** Always look for like terms and opportunities to cancel terms when simplifying expressions!

(x+6)^2 - (x-6)^2 + (x+4)^2 - (x-4)^2 - 40x

Learn how to simplify the expression (x+6)^2 - (x-6)^2 + (x+4)^2 - (x-4)^2 - 40x by expanding and combining like terms. This problem covers key algebraic concepts, including binomial expansion, difference of squares, and simplifying quadratic expressions. Suitable for students in Grades 8-10.

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