

\[
\left( x - \frac{3}{4} \right) \left( x + \frac{3}{4} \right)



To expand the given expression, we use the difference of squares formula:

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

In this case, \(a = x\) and \(b = \frac{3}{4}\). Applying the formula:

\[
\left( x - \frac{3}{4} \right) \left( x + \frac{3}{4} \right) = x^2 - \left( \frac{3}{4} \right)^2
\]

Now, calculate the square of \(\frac{3}{4}\):

\[
\left( \frac{3}{4} \right)^2 = \frac{9}{16}
\]

Substitute back into the expression:

\[
x^2 - \frac{9}{16}
\]

So, the expanded form of the expression is:

\[
x^2 - \frac{9}{16}
\]

Would you like more details on any steps, or do you have another question? 

### Follow-Up Questions:
1. How do you factor expressions like \(x^2 - \frac{9}{16}\)?
2. What is the difference of squares formula, and how is it used in different contexts?
3. Can you solve for \(x\) if the expression equals zero?
4. How does this expression change if we modify the constants?
5. What is the geometric interpretation of this quadratic expression?

**Tip:** Remember that the difference of squares formula is a quick way to factor and expand expressions involving two terms!

Learn how to expand the expression (x - 3/4)(x + 3/4) using the difference of squares formula. This problem covers key algebraic concepts and formulas, including the difference of squares theorem. Suitable for students in Grades 7-9.

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