(x-5)-multiply.jpeg "(x+5)(x-5) Multiply")
Multiplying (x + 5)(x - 5): A Breakdown
The expression (x + 5)(x - 5) is a product of two binomials. We can multiply them out using the FOIL method:
First: Multiply the first terms of each binomial: x * x = x² Outer: Multiply the outer terms of the binomials: x * -5 = -5x Inner: Multiply the inner terms of the binomials: 5 * x = 5x Last: Multiply the last terms of each binomial: 5 * -5 = -25
Now, let's add all these products together:
x² - 5x + 5x - 25
Notice that the middle terms (-5x and +5x) cancel each other out. This leaves us with:
x² - 25
This is the simplified form of (x + 5)(x - 5).
Why is this important?
This particular multiplication is a common example of the difference of squares pattern. This pattern occurs whenever you multiply two binomials where the only difference between them is the sign of the second term.
General Form: (a + b)(a - b) = a² - b²
Understanding this pattern allows you to quickly multiply these types of expressions without having to go through the full FOIL process.
Example
Let's say we want to multiply (2y + 3)(2y - 3).
Using the difference of squares pattern, we can directly determine the result:
(2y + 3)(2y - 3) = (2y)² - (3)² = 4y² - 9
This saves time and simplifies calculations.