expanding

Expanding is opening up a package: a product wrapped in parentheses gets unfolded into a sum of separate terms. If factoring is putting things into a box, expanding is taking them out and laying them flat.

The engine of expanding is the distributive property, which says a(b + c) = ab + ac — every term inside the parentheses gets multiplied by the factor outside. For a product of two binomials you multiply each term of the first by each term of the second (often remembered as FOIL): (x + 2)(x + 3) expands to x^2 + 5x + 6. Expanding and factoring are reverse operations.

Mind the signs when a negative multiplies a parenthesis: -(x - 4) expands to -x + 4, because the minus distributes onto both terms. Forgetting to multiply the second term, or dropping a sign, is the most common expanding error.