To derive the formula \((a+b)^2 - (a-b)^2 = 4ab\), we'll expand both squares and simplify the expression.

1. Expand \((a+b)^2\):
\[
(a+b)^2 = a^2 + 2ab + b^2
\]

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

3. Subtract the second expanded form from the first:
\[
(a+b)^2 - (a-b)^2 = (a^2 + 2ab + b^2) - (a^2 - 2ab + b^2)
\]

4. Distribute the negative sign in the subtraction:
\[
(a^2 + 2ab + b^2) - a^2 + 2ab - b^2
\]

5. Combine like terms:
\[
a^2 + 2ab + b^2 - a^2 + 2ab - b^2
\]

6. Simplify the combined terms:
\[
2ab + 2ab = 4ab
\]

Thus, we have derived that:
\[
(a+b)^2 - (a-b)^2 = 4ab
\]

Would you like any further details or have any questions about this derivation?

Here are 5 numbered questions you might ask next:
1. How do you derive the formula for \((a+b+c)^2\)?
2. Can you explain the difference of squares formula?
3. How do you prove the Quadratic Formula?
4. Can you solve and explain a cubic equation?
5. How do you find the integral of a polynomial function?

Tip: When working with algebraic expressions, always remember to apply and distribute signs carefully during expansion and simplification.

Learn how to derive the formula (a+b)^2 - (a-b)^2 = 4ab with a detailed step-by-step explanation. This problem covers algebraic concepts such as the expansion of squares and the difference of squares. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation