Let's simplify the expression:

Given:  
\[
50k - 2k(2k - 7)^2
\]

### Step 1: Expand the square term \((2k - 7)^2\).
\[
(2k - 7)^2 = (2k - 7)(2k - 7)
\]
Now, apply the distributive property (FOIL):
\[
(2k - 7)(2k - 7) = 4k^2 - 14k - 14k + 49 = 4k^2 - 28k + 49
\]

### Step 2: Substitute this back into the original expression:
\[
50k - 2k(4k^2 - 28k + 49)
\]

### Step 3: Distribute the \(2k\) across the terms inside the parentheses:
\[
50k - (2k \times 4k^2) + (2k \times 28k) - (2k \times 49)
\]
\[
= 50k - 8k^3 + 56k^2 - 98k
\]

### Step 4: Combine like terms:
\[
50k - 98k = -48k
\]
So, the expression simplifies to:
\[
-8k^3 + 56k^2 - 48k
\]

The final simplified expression is:
\[
-8k^3 + 56k^2 - 48k
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the general process for expanding binomials?
2. How do you factor out a common term in an expression like this?
3. What are the differences between cubic and quadratic terms?
4. How can you solve for \( k \) when given an equation with cubic terms?
5. How does the distributive property help in simplifying algebraic expressions?

**Tip:** Always expand powers and simplify before distributing terms for easier calculations!

Learn how to simplify the algebraic expression 50k - 2k(2k - 7)^2 with a step-by-step explanation. This solution includes polynomial expansion, the distributive property, and combining like terms. Suitable for students in Grades 9-12.

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