(x-10).jpeg "(x+10)(x-10)")
Understanding (x+10)(x-10)
The expression (x+10)(x-10) represents the product of two binomials. It can be simplified using the difference of squares pattern.
What is the Difference of Squares?
The difference of squares pattern is a useful algebraic identity:
(a + b)(a - b) = a² - b²
This pattern shows that the product of two binomials with the same terms but opposite signs is equal to the difference of the squares of those terms.
Applying the Pattern to (x+10)(x-10)
In this case, we have:
- a = x
- b = 10
Applying the difference of squares pattern:
(x + 10)(x - 10) = x² - 10²
Simplifying the Expression
Simplifying further, we get:
(x + 10)(x - 10) = x² - 100
Conclusion
Therefore, the simplified form of (x+10)(x-10) is x² - 100. This example demonstrates the usefulness of recognizing common algebraic patterns like the difference of squares, which can simplify complex expressions.