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Factorising Expressions Brackets mean multiply Extracting common factors means multiplying the HCF by each term in the brackets. 2x(3y + 4) = 6xy + 8x multiply 2x by each term inside the brackets 2x * 3y = 2 * 3 * x * y = 6 * x * y = 6xy Multiplying and dividing squares a X a = a2 a2 ÷ a = a 2 X 2 = 22 22 ÷ 2 = 2 22 = 4 4÷2=2 Factoring is reverse of removing brackets Expanding Remove brackets 5(2a+3)=10a+15 Factoring Put in brackets 10a+15=5(2a+3) Factorising is the reverse of Extracting To factorise a number means to break it up into numbers that can be multiplied together to get the original number The highest common factor HCF is the largest number that will divide into both numbers. Factorise by taking out the HCF. Example How to recognise it 5x + 20 2 terms Find the HCF and put it outside the How to factorise it Factors 5(x+4) brackets 5( ) Divide both terms by the HCF to find the factor inside the brackets 5x÷5=x ; 20÷5=4 grouping ac+bc+ad+bd 4 terms Bracket pairs of terms (ac+bc)+ (ad+bd) (c + d)(a + b) the terms Take the HCF fm each pair c(a+b)+d(a+b) Put the common factors in the 1st bracket quadratic x2 - 8x – 20 3 terms Find the factors of the third term (x+2)(x-10) trinomials a2 + a + n factors of -20 are … 1 x -20 = -20 ; 2 x -10 = -20 ; 4 x -5 = -20 5 x -4 = -20 ; 10 x -2 = -20 ; 20 x -1 = -20 Pick the factors which form the middle term when added 2+ -10 = -8 using the 25a2 – 16b2 square Find the square root of both terms (5a+4b)(5a-4b) Difference - square (5)2 = 25 : (a)2 = a2 : (4)2 = 16 : (b)2 = b2 of 2 Use the rule a2– b2 = (a–b)(a+b) squares Types of factorising Factorise by Example Factors taking out the HCF. 5x + 20 5(x+4) grouping the terms ac + bc + ad + bd (c + d)(a + b) quadratic trinomials x2 - 8x – 20 (x+2)(x-10) using the difference of 2 squares using the difference of 2 squares and hence evaluate 25a2 – 16b2 (5a+4b)(5a-4b) 62 - 52 (6+5)(6-5) = (11)(1) = 11 multiplied by 1 = 11