-(x%2B2).jpeg "(x-6) (x+2)")
Factoring and Expanding (x-6)(x+2)
The expression (x-6)(x+2) is a product of two binomials. We can simplify this expression by either expanding it or factoring it.
Expanding the Expression
To expand the expression, we use the distributive property (also known as FOIL method):
First: x * x = x² Outer: x * 2 = 2x Inner: -6 * x = -6x Last: -6 * 2 = -12
Combining the terms, we get: (x-6)(x+2) = x² + 2x - 6x - 12 = x² - 4x - 12
Factoring the Expression
If we are given the expression x² - 4x - 12, we can factor it into (x-6)(x+2).
To factor a quadratic expression, we look for two numbers that:
- Multiply to give the constant term (-12 in this case)
- Add to give the coefficient of the x term (-4 in this case).
The numbers -6 and 2 satisfy these conditions:
- -6 * 2 = -12
- -6 + 2 = -4
Therefore, we can factor the expression as (x - 6)(x + 2).
Conclusion
Both expanding and factoring the expression (x-6)(x+2) are important skills in algebra. Understanding these processes allows us to manipulate and simplify expressions, which is essential for solving equations and working with polynomials.