Which of the following expressions is equivalent to 25x2+16−40x−64y2?
(5x+4)2−64y2
(5x+8y)(5x−8y)−(40x+16)
(5x−8y)2+16
(5x−4)2−64y2
               
 

Let's start by simplifying the original expression \( 25x^2 + 16 - 40x - 64y^2 \).

### Step 1: Group the terms involving \(x\) and \(y\).
The given expression is:
\[
25x^2 - 40x + 16 - 64y^2
\]
We will group the terms as follows:
\[
(25x^2 - 40x + 16) - 64y^2
\]

### Step 2: Factor the quadratic expression \(25x^2 - 40x + 16\).
The expression \(25x^2 - 40x + 16\) can be factored as a perfect square:
\[
25x^2 - 40x + 16 = (5x - 4)^2
\]
Thus, the expression becomes:
\[
(5x - 4)^2 - 64y^2
\]

### Step 3: Recognize the form of a difference of squares.
Now, notice that we have a difference of squares:
\[
(5x - 4)^2 - (8y)^2
\]
This matches the structure of the fourth option:
\[
(5x - 4)^2 - 64y^2
\]

Thus, the expression is equivalent to:

\[
\boxed{(5x - 4)^2 - 64y^2}
\]

Would you like a breakdown of factoring techniques?  
Here are 5 related questions you can explore:
1. How do you factor a perfect square trinomial?
2. What is the difference of squares formula?
3. How do you factor \(a^2 - b^2\)?
4. Can you apply the difference of squares to more complex expressions?
5. How do you expand binomials like \((5x - 4)^2\)?

**Tip:** When simplifying quadratic expressions, always check for common factoring patterns like perfect square trinomials or the difference of squares.

Which of the following expressions is equivalent to 25x^2 + 16 − 40x − 64y^2?
(5x+4)^2−64y^2
(5x+8y)(5x−8y)−(40x+16)
(5x−8y)^2+16
(5x−4)^2−64y^2

This page provides a step-by-step guide to simplify the expression 25x^2 + 16 - 40x - 64y^2. It explains how to factor perfect square trinomials and apply the difference of squares formula, making it suitable for students in Grades 9-11.

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