(x-4).jpeg "(x-3)(x-4)")
Expanding (x-3)(x-4)
In algebra, we often encounter expressions like (x-3)(x-4). This expression represents the product of two binomials, and it can be expanded using the FOIL method. FOIL stands for First, Outer, Inner, Last, which describes the order in which we multiply the terms of the binomials.
Here's how to expand (x-3)(x-4) using the FOIL method:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * -4 = -4x
- Inner: Multiply the inner terms of the binomials: -3 * x = -3x
- Last: Multiply the last terms of each binomial: -3 * -4 = 12
Now, we have the following expression:
x² - 4x - 3x + 12
Finally, combine the like terms:
x² - 7x + 12
Therefore, the expanded form of (x-3)(x-4) is x² - 7x + 12.
Understanding the Process
Expanding binomials like this is a fundamental concept in algebra. It's important to understand how the FOIL method works, as it provides a systematic way to multiply binomials and simplify expressions.
This process is also useful for solving equations and working with quadratic expressions.
Further Exploration
Once you've mastered the FOIL method, you can explore more complex binomial multiplications, such as those involving variables with exponents or coefficients. You can also learn how to factor quadratic expressions like x² - 7x + 12 back into their original binomial form.