Combining like terms, but more complicated | Introduction to algebra | Algebra I | Khan Academy

The video starts by presenting a complicated algebraic expression and highlights that terms with different variable parts, even if they share a letter (like 'y' and 'xy'), cannot be combined. It uses numerical examples to illustrate why 'y', 'xy', and 'y²' are distinct.

The presenter reorders the expression, grouping terms with identical variable components. For example, all 'y' terms are grouped together, all 'xy' terms, all 'x²' terms, and so on. This color-coded reordering makes the simplification process clearer.

The 'y' terms, -3y and +2y, are combined. By adding their coefficients (-3 + 2), they simplify to -1y or simply -y.

The 'xy' terms, +4xy and -4xy, are combined. Their coefficients (4 - 4) sum to 0, meaning these terms cancel each other out and result in 0xy or simply 0.

The 'x²' terms, -2x² and +3x², are combined. Adding their coefficients (-2 + 3) results in 1x², which simplifies to x².

The remaining terms, +2x and +y², have no like terms to combine with. The final simplified expression is -y + x² + 2x + y². The order of these terms does not affect the correctness of the answer.