Expanding Brackets

Expanding brackets (distribution) “untangles” expressions by multiplying each term inside parentheses by the factor outside. This turns grouped expressions into a sum of separate terms, paving the way for combining like terms or moving everything to one side of an equation.

You’ll often see puzzles where several brackets are nested or accompanied by plus/minus signs, so systematic expansion is critical. Ignoring minus signs in front of brackets is a common source of errors – always distribute the sign as well as any coefficient.

Example: Expand (x + 4)(x – 3)

1. Multiply x by each term in the second bracket: x² – 3x
2. Multiply 4 by each term: 4x – 12
3. Combine: x² − 3x + 4x − 12 = x² + x − 12

Hints and tips

• Apply the distributive law systematically: For (a + b)(c + d), always multiply a × c, a × d, b × c, then b × d in order.
• Mind minus signs: If you have −(x + 3), rewrite as – x – 3 so the sign flip is explicit.
• Keep each product on its own line (at first): Write x², on one line, then −3x etc., before summing.
• Combine immediately afterward: Once all four products are listed, combine like terms to prevent misplacement.
• Practice FOIL for binomials: Remember First, Outer, Inner, Last for quick two-term expansions.