What is Expanding? — Mathematics

Definition 66.1 Primary & Middle School Mathematics · Chapter 66 — Algebra and Equations

Expanding means transforming a product into a sum, using distributivity:

k(a + b) = ka + kb, \qquad (a + b)(c + d) = ac + ad + bc + bd .

Examples

Example 66.2

Every term of the first bracket multiplies every term of the second:

\begin{align*} (x + 3)(2x + 5) &= x \times 2x + x \times 5 + 3 \times 2x + 3 \times 5 \\ &= 2x^2 + 5x + 6x + 15 \\ &= 2x^2 + 11x + 15 . \end{align*}

Signs travel with the terms:

\begin{align*} (3x - 2)(x - 4) &= 3x^2 - 12x - 2x + 8 = 3x^2 - 14x + 8 . \end{align*}