Expanding Single Brackets

Multiply the term outside by EVERYTHING inside.

Formula: a(b + c) = ab + ac

Example: 3(x + 4) = 3x + 12 -2(5y - 3) = -10y + 6

Collecting Like Terms

Combine parts with identical letters and powers.

Example: 3x + 2y + 5x - y = 8x + y

Negative Terms

Be extremely careful with negatives when expanding.

Multi-term Brackets

The rule is the same regardless of how many terms are inside.

Example: 5(x + y - z) = 5x + 5y - 5z

Algebraic Terms Outside

When a variable is outside, remember x × x = x².

Example: x(x + 3) = x² + 3x

Double Brackets (FOIL)

First, Outer, Inner, Last.

Formula: (a+b)(c+d) = ac + ad + bc + bd

Example: (x + 3)(x + 5) = x² + 8x + 15

Triple Brackets

Expand two brackets first, then multiply the result by the third.

Difference of Two Squares (DOTS)

Middle terms cancel out. Always gives x² - n².

Formula: (x+a)(x-a) = x² - a²

Example: (x+5)(x-5) = x² - 25

Squaring a Bracket

It means multiplying it by itself. (x+3)² is NOT x²+9.

Formula: (a+b)² = a² + 2ab + b²

Example: (x+3)² = (x+3)(x+3) = x² + 6x + 9

Negative Coefficients

Be careful with (x−3)². It expands to x² − 6x + 9.