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(x+2)(x+9)

2 min read Jun 16, 2024
(x+2)(x+9)

Expanding the Expression (x+2)(x+9)

This expression represents the multiplication of two binomials: (x+2) and (x+9). To expand it, we can use the FOIL method, which stands for First, Outer, Inner, Last. Here's how it works:

FOIL Method

  1. First: Multiply the first terms of each binomial: x * x = x²
  2. Outer: Multiply the outer terms of the binomials: x * 9 = 9x
  3. Inner: Multiply the inner terms of the binomials: 2 * x = 2x
  4. Last: Multiply the last terms of each binomial: 2 * 9 = 18

Now, we have: x² + 9x + 2x + 18

Simplifying the Expression

Finally, combine the like terms (the terms with 'x'):

x² + 11x + 18

Therefore, the expanded form of (x+2)(x+9) is x² + 11x + 18.

Further Applications

This expanded form can be used in various mathematical applications such as:

  • Solving equations: Setting the expression equal to zero and solving for x can find the roots of the equation.
  • Graphing functions: The expanded form allows you to easily plot the graph of the function represented by the expression.
  • Factoring: Understanding how to expand binomials is crucial for factoring quadratic expressions.

This example demonstrates a fundamental concept in algebra: expanding and simplifying expressions. By mastering this skill, you can confidently tackle more complex mathematical problems.

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