(a+b)(a-b) Simplify

2 min read Jun 16, 2024
(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.

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