(x-5)-answer.jpeg "(x+5)(x-5) Answer")
Understanding (x+5)(x-5)
The expression (x+5)(x-5) represents a product of two binomials. To find the answer, we can use the FOIL method, which stands for First, Outer, Inner, Last.
Expanding the Expression
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms: x * -5 = -5x
- Inner: Multiply the inner terms: 5 * x = 5x
- Last: Multiply the last terms: 5 * -5 = -25
This gives us the following expanded expression:
x² - 5x + 5x - 25
Simplifying the Expression
Notice that the middle terms, -5x and 5x, cancel each other out. This leaves us with:
x² - 25
The Difference of Squares Pattern
The expression (x² - 25) is a difference of squares. This pattern occurs when you have two perfect squares (x² and 25) separated by a minus sign. The general form of this pattern is:
(a² - b²) = (a + b)(a - b)
In our case, a = x and b = 5. Therefore, (x² - 25) can be factored back into the original expression:
(x + 5)(x - 5)
Conclusion
The answer to (x+5)(x-5) is x² - 25. This example demonstrates the difference of squares pattern, a useful tool in factoring and simplifying algebraic expressions.