Algebra 101 - Unit 1

Simplifying Algebraic Expressions

Simplifying algebraic expressions means rewriting them in a simpler or more compact form without changing their value. This is a key skill in Algebra 1, as it makes equations easier to work with and solve.

1. Combine Like Terms

Like terms have the same variable raised to the same power. Only like terms can be combined by addition or subtraction.

• Example: 3x + 5x = 8x
• Example: 2y + 7 - 3y + 4 = -y + 11

2. Use the Distributive Property

Multiply a single term by each term inside parentheses to remove the parentheses.

• Example: 2(x + 3) = 2·x + 2·3 = 2x + 6
• Example: 5(2y - 4) = 10y - 20

3. Simplify Step by Step

Always work systematically using the order of operations (PEMDAS) when simplifying expressions with multiple operations.

• Example: Simplify 3(x + 2) + 4x
1. Distribute: 3x + 6 + 4x
2. Combine like terms: 3x + 4x + 6 = 7x + 6

4. Simplify Expressions with Negative Signs

• Example: 5 - (2x + 3) = 5 - 2x - 3 = -2x + 2
• Example: -3(2y - 5) = -6y + 15

5. Combine Multiple Steps

Some expressions require both the distributive property and combining like terms.

• Example: Simplify 2(x + 3) + 4(x - 2) + 5
1. Distribute: 2x + 6 + 4x - 8 + 5
2. Combine like terms: (2x + 4x) + (6 - 8 + 5) = 6x + 3

6. Tips for Success

• Identify and combine like terms carefully.
• Use the distributive property to eliminate parentheses.
• Pay attention to negative signs and subtraction.
• Simplify step by step—don’t skip operations.

Simplifying algebraic expressions is a foundation skill that will make solving equations, factoring, and working with more advanced algebra concepts much easier.