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(x+4)(x+5) Expand And Simplify

2 min read Jun 16, 2024
(x+4)(x+5) Expand And Simplify

Expanding and Simplifying (x+4)(x+5)

This article will guide you through the process of expanding and simplifying the expression (x+4)(x+5).

Understanding the Process

Expanding a product of binomials like (x+4)(x+5) involves applying the distributive property. This means multiplying each term in the first binomial by each term in the second binomial.

Step-by-Step Expansion

  1. Multiply the first terms:

    • x * x = x²

  2. Multiply the outer terms:

    • x * 5 = 5x

  3. Multiply the inner terms:

    • 4 * x = 4x

  4. Multiply the last terms:

    • 4 * 5 = 20

  5. Combine all the terms:

    • x² + 5x + 4x + 20

  6. Simplify by combining like terms:

    • x² + 9x + 20

Final Result

Therefore, the expanded and simplified form of (x+4)(x+5) is x² + 9x + 20.

Key Concepts

  • Distributive Property: This property states that a(b+c) = ab + ac. It's crucial for expanding products of binomials.
  • Combining Like Terms: Terms with the same variable and exponent can be added or subtracted. This simplifies the expression.

By understanding the distributive property and combining like terms, you can confidently expand and simplify any product of binomials.

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