What if it’s a square of a difference what di you do there ?

When you encounter the **square of a difference**, it refers to an expression of the form:

\[
(a - b)^2
\]

To simplify or expand this expression, you apply the distributive property (also known as FOIL: First, Outer, Inner, Last). The general formula for the square of a difference is:

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

### Here's a step-by-step breakdown:

1. **Square the first term**: \(a^2\)
2. **Multiply the two terms together and double it**: \(-2ab\)
3. **Square the second term**: \(b^2\)

Putting it all together:

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

This formula is a common identity in algebra and helps simplify expressions where differences are squared.

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Do you need more details on this? Here are some questions to explore further:

1. What happens if \(a\) and \(b\) are complex numbers?
2. How does the square of a sum differ from the square of a difference?
3. Can you apply this identity to solve quadratic equations?
4. How would you factor the expanded form back into its original?
5. How is this formula used in completing the square?

**Tip**: Always double-check the middle term when expanding a binomial square—it’s easy to forget to multiply by 2!

What if it’s a square of a difference what do you do there?

Learn how to simplify and expand the square of a difference, (a - b)^2, using the distributive property. This algebra problem involves binomial expansion, resulting in a^2 - 2ab + b^2, and is suitable for students in Grades 8-10.

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