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.