To simplify the expression \((2X + 4)^2\), we can use the formula for the square of a binomial, which is:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

Here, \(a = 2X\) and \(b = 4\). Let's expand it:

\[
(2X + 4)^2 = (2X)^2 + 2(2X)(4) + (4)^2
\]

Now calculate each term:

\[
(2X)^2 = 4X^2
\]
\[
2(2X)(4) = 16X
\]
\[
(4)^2 = 16
\]

So, the expanded form is:

\[
(2X + 4)^2 = 4X^2 + 16X + 16
\]

This is the simplified expression.

Would you like further details or have any questions?

### 5 Related Questions:
1. How do you factor the expression \(4X^2 + 16X + 16\)?
2. What is the geometric meaning of squaring a binomial?
3. How would the result change if you had \((2X - 4)^2\) instead?
4. Can you explain the connection between this expansion and completing the square in quadratics?
5. How does this relate to solving quadratic equations?

### Tip:
Remember that the square of a binomial always follows the same pattern: square the first term, double the product of both terms, and square the second term.

Learn how to expand and simplify the binomial expression (2X + 4)² using the binomial expansion formula. This guide explains each step in detail and covers essential algebraic concepts suitable for students in Grades 8-10.

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