GCSE›AQA GCSE Maths›Mind mapsAlgebraic ManipulationAQA GCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsNotationababab means a×ba \times ba×bIn 2a2a2a, the coefficient is 2Terms are separated by + or −Like terms have identical letters and powers3x3x3x and 3x23x^23x2 are not like termsCollecting termsAdd or subtract the coefficients2xy−5xy=−3xy2xy - 5xy = -3xy2xy−5xy=−3xy3x+2y3x + 2y3x+2y cannot be simplifiedGroup like terms firstExpand and factoriseMultiply every term inside the bracket−2(a−3)=−2a+6-2(a - 3) = -2a + 6−2(a−3)=−2a+6(x+3)(x+2)=x2+5x+6(x+3)(x+2) = x^2 + 5x + 6(x+3)(x+2)=x2+5x+6Factorise using the HCF: 6x+9=3(2x+3)6x + 9 = 3(2x+3)6x+9=3(2x+3)a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b)a2−b2=(a+b)(a−b)Algebramanipulationab2aa2a^2a2Quadraticsx2+bx+cx^2 + bx + cx2+bx+c: numbers that multiply to ccc, add to bbbx2+5x+6=(x+2)(x+3)x^2 + 5x + 6 = (x+2)(x+3)x2+5x+6=(x+2)(x+3)Completing the square: (x+b2)2−(b2)2+c(x + \frac{b}{2})^2 - (\frac{b}{2})^2 + c(x+2b)2−(2b)2+cx2+6x+5=(x+3)2−4x^2 + 6x + 5 = (x+3)^2 - 4x2+6x+5=(x+3)2−4Fractions and formulaeFactorise, then cancel common factorsCommon denominator: ab+cd=ad+bcbd\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}ba+dc=bdad+bcRearrange using inverse operationsSubject twice: collect it on one sideSubstitute following BIDMASExam tipsMultiply out brackets to check factorising3x+2y≠5xy3x + 2y \neq 5xy3x+2y=5xyMatch factors in the right bracketsState restrictions like x≠2x \neq 2x=2