Definition
Expand an expression
Expand an expression by multiplying through its grouping to make an equivalent sum or difference.
What it means
Think of the factor outside the brackets as having to reach every term inside. Multiply it by each term and keep the signs. You are not finding one answer; you are rewriting the same expression in an equal form.
Remember it
The outside factor visits every term inside the brackets.
Example
Expand 4(2x − 3). Multiply 4 by both terms: 4 × 2x = 8x and 4 × (−3) = −12. Therefore, 4(2x − 3) = 8x − 12.
Watch for
Multiplying only the first term is not expansion: 4(2x − 3) is not 8x − 3 because the factor 4 must reach both terms.
Common mix-up
Expanding opens a product into a sum or difference. Factorising travels in the opposite direction by packing terms into a product.
Exact meaning
Expanding an expression rewrites a product containing brackets or parentheses as an equivalent sum or difference by applying the distributive property to every term in the group.