Section 1.3: Simplifying Expressions
To simplify an expression means to rewrite it in its simplest form by combining like terms and applying the distributive property when needed.
Rules for Simplifying:
- Like Terms have the same variable(s) raised to the same power (e.g., \( 3x \) and \( -5x \) are like terms).
- Combine like terms by adding/subtracting their coefficients.
- Use the Distributive Property: \( a(b + c) = ab + ac \).
Example 1
Simplify: \( 4x + 7x - 3 \).
Combine like terms: \( 4x + 7x = 11x \).
So, the simplified expression is: \( 11x - 3 \).
Example 2
Simplify: \( 2(3x + 4) - x \).
Apply distributive property: \( 2(3x + 4) = 6x + 8 \).
Now subtract \( x \): \( 6x + 8 - x = 5x + 8 \).
Final answer: \( 5x + 8 \).
Practice Problems
- Simplify: \( 7y + 2y - 5 \).
- Simplify: \( 3(a + 2) + 4a \).
- Combine like terms: \( 5x + 3 - 2x + 6 \).
- Use distributive property: \( 4(2m - 3) + m \).
- Simplify completely: \( 6p + 2(p - 4) \).