(x-9)-answer.jpeg "(x+9)(x-9) Answer")
Expanding (x+9)(x-9)
The expression (x+9)(x-9) represents the product of two binomials. To find the answer, we can use the FOIL method:
First: Multiply the first terms of each binomial.
x * x = x²
Outer: Multiply the outer terms of the binomials.
x * -9 = -9x
Inner: Multiply the inner terms of the binomials.
9 * x = 9x
Last: Multiply the last terms of each binomial.
9 * -9 = -81
Now, combine all the terms:
x² - 9x + 9x - 81
Notice that the middle terms (-9x and 9x) cancel each other out:
x² - 81
Therefore, the expanded form of (x+9)(x-9) is x² - 81.
Important Note:
This specific expression, (x+9)(x-9), is an example of a difference of squares. This pattern is important to recognize:
- (a + b)(a - b) = a² - b²
In our case, a = x and b = 9. Understanding the difference of squares pattern allows for quick and efficient expansion of similar expressions.