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.
StepbyStep Expansion

Multiply the first terms:
 x * x = x²

Multiply the outer terms:
 x * 5 = 5x

Multiply the inner terms:
 4 * x = 4x

Multiply the last terms:
 4 * 5 = 20

Combine all the terms:
 x² + 5x + 4x + 20

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.