(a-b)-simplify.jpeg "(a+b)(a-b) Simplify")
Simplifying the Expression (a + b)(a - b)
The expression (a + b)(a - b) is a common algebraic expression that simplifies to a much simpler form. This simplification is based on the difference of squares pattern.
Understanding the Difference of Squares
The difference of squares pattern states that: (x + y)(x - y) = x² - y²
This pattern can be understood by expanding the expression:
- (x + y)(x - y) = x(x - y) + y(x - y)
- = x² - xy + xy - y²
- = x² - y²
Applying the Pattern to (a + b)(a - b)
Applying the difference of squares pattern to our expression (a + b)(a - b), we can see that:
- a corresponds to x
- b corresponds to y
Therefore, we can simplify the expression as:
(a + b)(a - b) = a² - b²
Example:
Let's say a = 3 and b = 2. We can use the simplified form to calculate the value of the expression:
(a + b)(a - b) = a² - b² (3 + 2)(3 - 2) = 3² - 2² (5)(1) = 9 - 4 5 = 5
As you can see, the simplified form makes the calculation much easier.
Conclusion
Simplifying expressions like (a + b)(a - b) using the difference of squares pattern is a valuable skill in algebra. It allows us to manipulate expressions more easily and solve equations more efficiently.