Algebra 1 / Unit 1: Expressions and Real Numbers
1.4 Like Terms and the Distributive Property
Notes
Like terms have the same variables raised to the same powers: $3x$ and $-7x$ are like terms; $3x$ and $3x^2$ are not.
- Combine like terms by adding their coefficients: $5y + 2y - y = 6y$.
- Distributive property: $a(b + c) = ab + ac$. Multiply the outside number by every term inside.
- Distribute a negative carefully: $-2(x - 4) = -2x + 8$.
Practice
Simplify $4x + 3 - 6x + 9$.
$4x - 6x = -2x$ and $3 + 9 = 12$.
Simplify $-3(2y - 5)$.
$-3 \cdot 2y = -6y$ and $-3 \cdot (-5) = +15$.
Simplify $5(a + 2) - 2(a - 1)$.
$5a + 10 - 2a + 2 = 3a + 12$.
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