� Single brackets — basic
Expand expressions like \(3(x+4)\) and \(4(3x-8)\). Multiply every term inside by the factor outside.
� Single brackets — negative factors
Expand with negative outside factors like \(-2(x-5)\). Watch every sign change.
� Expand and simplify
Expand two brackets then collect like terms: \(4(3x-8)+2(x+1)\) or \(5(5-6x)-4(x-7)\).
� Brackets with powers — linear × linear variable
Expressions like \(x(2x-3)\) giving terms in \(x^2\).
� Brackets with powers — higher powers
Expressions like \(2x^2(3x^2-5x+3)\) giving terms in \(x^4\), \(x^3\) etc.
� Double brackets
Expand \((x+a)(x+b)\) using FOIL or the grid method.
Key rules
Single bracket: multiply every term inside by the term outside. \(a(bx+c)=abx+ac\)
Negative factor: multiplying by a negative flips every sign. \(-2(x-5)=-2x+10\)
Powers: add the indices when multiplying. \(x\times x^2=x^3\), \(2x^2\times3x=6x^3\)
Double brackets: each term in the first bracket multiplies each term in the second.