Algebraic Expressions & Simplifying

Why This Matters for Nursing: Dosing formulas often contain variables. "Dose = Weight × 2.5 + 10" is an algebraic expression. Understanding how to read and simplify these helps you use medical formulas correctly.

What You Need to Know

An algebraic expression combines numbers, variables, and operations: - Variable: A letter representing an unknown value (x, y, n, w) - Coefficient: The number multiplied by a variable (in 3x, the coefficient is 3) - Constant: A number without a variable (in 3x + 5, the constant is 5) - Term: Parts separated by + or - signs (in 3x + 5, there are 2 terms)

Like Terms

Like terms have the same variable raised to the same power: - 3x and 5x are like terms ✓ - 3x and 3x² are NOT like terms ✗ - 4 and 7 are like terms (both constants) ✓

🧠 Memory Trick

"Combine the Cousins"

Like terms are like family members—you can only combine (add/subtract) terms that are "related" (same variable, same power).

3x + 5x = 8x ✓ (cousins!) 3x + 5y = 3x + 5y (strangers, can't combine)

Simplifying Expressions

Step-by-Step:

1. Identify like terms (same variable, same power)
2. Combine like terms by adding/subtracting coefficients
3. Write in standard form (highest power first, or alphabetical)

Example: Simplify 4x + 3 + 2x - 7

1. Group like terms: (4x + 2x) + (3 - 7)
2. Combine: 6x + (-4) 3.