GCSE›Edexcel GCSE Maths›Mind mapsAlgebraic ManipulationEdexcel GCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsLike termsSame letter, same powerGroup, then add coefficients4x+3y−2x+5y+1=2x+8y+14x + 3y - 2x + 5y + 1 = 2x + 8y + 14x+3y−2x+5y+1=2x+8y+12x2x2x and 2x22x^22x2 are not like termsExpandingSingle: multiply every term inside3(2x+5)=6x+153(2x+5) = 6x + 153(2x+5)=6x+15Double: FOIL or grid method(x+2)(x+3)=x2+5x+6(x+2)(x+3) = x^2 + 5x + 6(x+2)(x+3)=x2+5x+6Triple: expand two, then the thirdCommon factorTake out the greatest common factor6x2+9x=3x(2x+3)6x^2 + 9x = 3x(2x+3)6x2+9x=3x(2x+3)12a3b+8ab2=4ab(3a2+2b)12a^3b + 8ab^2 = 4ab(3a^2+2b)12a3b+8ab2=4ab(3a2+2b)Check by expanding backManipulationexpand and factorisex2x^2x2(x+a)(x+a)(x+a)QuadraticsDifference of two squares: x2−a2=(x+a)(x−a)x^2 - a^2 = (x+a)(x-a)x2−a2=(x+a)(x−a)x2+7x+12=(x+3)(x+4)x^2+7x+12 = (x+3)(x+4)x2+7x+12=(x+3)(x+4)Two numbers: add to bbb, multiply to cccax2+bx+cax^2+bx+cax2+bx+c: find numbers multiplying to acacac2x2+7x+3=(2x+1)(x+3)2x^2+7x+3 = (2x+1)(x+3)2x2+7x+3=(2x+1)(x+3)Algebraic fractionsFactorise, then cancel factorsx2−4x+2=x−2\frac{x^2-4}{x+2} = x - 2x+2x2−4=x−2Add: find a common denominatorDivide: flip the second and multiplyExam tipsCancel factors, never termsx2+25x^2 + 25x2+25 does not factorise this waySign errors: inner term of (x−3)(x+2)(x-3)(x+2)(x−3)(x+2) is −3x-3x−3x