Like terms and the distributive law

Like terms have exactly the same variable part, including powers. Their coefficients can be added: \(5x-2x=3x\), but \(x+x^2\) cannot be combined. Distributing means multiplying every term inside a bracket by the outside factor.

Example

\(\begin{aligned}-2(3x-5)+4x&=-6x+10+4x\\&=-2x+10\end{aligned}\)

With fractions, first use a common denominator: \(\begin{aligned}\dfrac{x+3}{6}+\dfrac{x}{2}&=\dfrac{x+3+3x}{6}\\&=\dfrac{4x+3}{6}.\end{aligned}\)

Check the sign of every term when removing a bracket preceded by a minus. The minus applies to the entire bracket.