S1 · Algebra · ALG.LIKE.TERMS

Combine like terms

Intuition

Understand first, compress later.

Algebra describes structures generally: a symbol stands for a number, while the rules remain the same.

Switch representations

Area modelDistributive law

The rectangle is 3 high and 2x wide. Its area reads once as height times bracket and once as the two blocks added — that is exactly the distributive law.

Formal view

You can combine like terms when you can recognise the underlying objects, select valid rules and check each step for equivalence or logical implication.

Why does it work?

This skill sits on a prerequisite network. If a step is unstable, repair the missing prerequisite instead of merely doing more items of the same type.