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Factorisation David Weeks © Mathsmadeeasy Permission given to use for non-commercial use 4 + 8 + 12 4x + 8x + 12x 2t + t 3 4y 2 + 8y 3 Alter animation effects as appropriate

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factorisation 4 + 8+ 12 2 is a factor which goes into them but 4 is a bigger factor. Use that! Rewrite them all with the factor 4 4 x 1 + 4 x 2 + 4 x 3 Now add the brackets and move the factor 4 outside it to the front ( ) 4 Now put the rest of each multiplication inside the brackets 1 + 2 + 3 Thats it – we have factorised! = 4 (6) = 24 = 24 First find a common factor Lets factorise this simple sum 4 + 8 +12 ( ) 4 1 + 2 + 3 = Simplify to check ( ) 4 1 + 2 + 3

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factorisation 4 x + 8 x + 12 x 2 x is a factor which goes into them but 4 x is a bigger factor. Use that! Rewrite them all with the factor 4 x 4 x x 1 + 4 x x 2 + 4 x x 3 Now add the brackets and move the factor 4 x outside it to the front ( ) 4x4x Now put the rest of each multiplication inside the brackets 1 + 2 + 3 Thats it – we have factorised! = 24 x First find a common factor Lets factorise this simple sum 4 x + 8 x +12 x = 4 x ( 1 + 2 + 3 ) Simplify to check 4 x ( 1 + 2 + 3 ) = 4 x (6)

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factorisation 2 t + t 3 t appears in both terms so its a factor. Use that! Add the brackets and move the factor t outside it to the front ( ) t Now put the rest of each multiplication inside the brackets 2 + t x t First find a common factor Expand the terms Lets factorise this simple sum Thats it – we have factorised! 2 t + t 3 = t ( 2 + t 2 ) 2 x t + t x t x t Look for repeating terms t ( 2 + t 2 )

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factorisation 4 y 2 + 8 y 3 4 x y x y = 4 y 2 appears in both terms so its a factor. Use that! Add the brackets and move the factor 4 y 2 outside it to the front ( ) 4y24y2 Now put the rest of each multiplication inside the brackets 1 + 2 x y First find a common factor Expand the terms Lets factorise this simple sum Thats it – we have factorised! 4 y 2 + 8 y 3 = 4 y 2 ( 1 + 2 y ) 4 x y x y x 1 + 4 x 2 x y x y x y Look for repeating terms 4 y 2 ( 1 + 2 y )

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