What are the steps to solve

Solving $(A-B)^2$ involves expanding the expression using the binomial theorem. This is a fundamental algebraic technique that helps simplify and solve polynomial expressions. Let’s walk through the steps to solve $(A-B)^2$

Step-by-Step Solution

1. Understand the Binomial Theorem
   The binomial theorem provides a way to expand expressions that are raised to a power. For the expression $(A-B)^2$, we use the specific case of the binomial theorem for a power of 2.

2. Apply the Binomial Expansion Formula
   The binomial expansion formula for $(A-B)^2$ is:

   $(A-B)^2 = A^2 – 2AB + B^2$

3. Break Down Each Term
   Let’s break down each term in the expanded form:
   • $A^2$: This is the square of the first term, A.
   • $-2AB$: This is twice the product of the first term (A) and the second term (B). The negative sign comes from the subtraction in the original expression.
   • $B^2$: This is the square of the second term, B.

4. Combine the Terms
   After breaking down each term, we combine them to get the expanded form:

   $A^2 – 2AB + B^2$

Example

Let’s take an example to make it clearer. Suppose we have $(3-2)^2$

1. Identify A and B: Here, A = 3 and B = 2.
2. Apply the formula:

$(3-2)^2 = 3^2 – 2(3)(2) + 2^2$

3. Calculate each term:
   • $3^2 = 9$
   • $2(3)(2) = 12$
   • $2^2 = 4$
4. Combine the terms:

$9 – 12 + 4 = 1$

So, $(3-2)^2 = 1$

Conclusion

By following these steps, you can expand and simplify any expression of the form $(A-B)^2$. This technique is useful in various areas of algebra and helps build a strong foundation for more complex mathematical concepts.

Citations

1. 1. Khan Academy – Binomial Theorem
2. 2. Purplemath – Binomial Squares
3. 3. Math is Fun – Binomial Theorem