(x-2)(x-4)

2 min read Jun 17, 2024

Expanding and Simplifying (x-2)(x-4)

This article will guide you through expanding and simplifying the expression (x-2)(x-4). We'll use the FOIL method to achieve this.

What is FOIL?

FOIL stands for First, Outer, Inner, Last. It's a mnemonic device used to remember the steps involved in multiplying two binomials.

Applying FOIL to (x-2)(x-4)

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: -2 * x = -2x
Last: Multiply the last terms of each binomial: -2 * -4 = 8

Combining the Terms

Now, we have: x² - 4x - 2x + 8

Finally, combine the like terms: x² - 6x + 8

Conclusion

Therefore, the expanded and simplified form of (x-2)(x-4) is x² - 6x + 8.

This method of expansion is crucial for working with quadratic equations and solving problems in algebra. By understanding the FOIL method, you can easily multiply any two binomials and simplify the resulting expression.