(x+1)(x+2) Expand And Simplify

2 min read Jun 16, 2024

Expanding and Simplifying (x+1)(x+2)

This article will guide you through the process of expanding and simplifying the expression (x+1)(x+2).

Understanding the Process

Expanding a product of binomials like this involves using the distributive property (often referred to as FOIL). Here's how it works:

First: Multiply the first terms of each binomial.
Outer: Multiply the outer terms of the binomials.
Inner: Multiply the inner terms of the binomials.
Last: Multiply the last terms of each binomial.

Expanding (x+1)(x+2)

Let's apply the FOIL method:

First: (x) * (x) = x²
Outer: (x) * (2) = 2x
Inner: (1) * (x) = x
Last: (1) * (2) = 2

Now, we have: x² + 2x + x + 2

Simplifying the Expression

The final step is to combine like terms:

x² + 3x + 2

Conclusion

Therefore, the expanded and simplified form of (x+1)(x+2) is x² + 3x + 2. This process demonstrates how to effectively expand and simplify binomial expressions, which is a fundamental skill in algebra.