(x+4)(x+5) In Standard Form

2 min read Jun 16, 2024

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) into its standard form.

Understanding the Problem

The expression (x+4)(x+5) represents the product of two binomials. To express it in standard form, we need to multiply the terms within the parentheses and combine like terms.

Expanding the Expression

We can use the FOIL method to expand the expression:

First: Multiply the first terms of each binomial: x * x = x²
Outer: Multiply the outer terms of each binomial: x * 5 = 5x
Inner: Multiply the inner terms of each binomial: 4 * x = 4x
Last: Multiply the last terms of each binomial: 4 * 5 = 20

This gives us: x² + 5x + 4x + 20

Simplifying the Expression

Now, we combine the like terms:

x² + (5x + 4x) + 20

This simplifies to:

x² + 9x + 20

Standard Form

The standard form of a quadratic expression is ax² + bx + c, where a, b, and c are constants.

Therefore, the standard form of the expression (x+4)(x+5) is x² + 9x + 20.