(x-12).jpeg "(x+7)(x-12)")
Expanding the Expression (x + 7)(x - 12)
This expression represents the product of two binomials: (x + 7) and (x - 12). To expand it, we can use the FOIL method, which stands for First, Outer, Inner, Last.
Here's how it works:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * -12 = -12x
- Inner: Multiply the inner terms of the binomials: 7 * x = 7x
- Last: Multiply the last terms of each binomial: 7 * -12 = -84
Now, combine the terms: x² - 12x + 7x - 84
Finally, simplify by combining like terms:
x² - 5x - 84
Therefore, the expanded form of (x + 7)(x - 12) is x² - 5x - 84.
Why is this important?
Expanding binomials like this is a fundamental skill in algebra. It's essential for:
- Solving quadratic equations: The expanded form can be used to find the roots of a quadratic equation.
- Factoring polynomials: Understanding the expansion process helps us to reverse engineer and factorize polynomials.
- Simplifying expressions: Expanding can make complicated expressions easier to work with.
By mastering the FOIL method, you build a solid foundation for more advanced algebraic concepts.