3 ( x + 2 ) = 3 x + 6 2 ( 3 x - 5 ) = 6x - 10 xxx - 5 M May.

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Presentation transcript:

3 ( x + 2 ) = 3 x ( 3 x - 5 ) = 6x - 10 xxx - 5 M May

2x + 6 2x = 2 x x 6 = 2 x 3 = 2 ( x + 3 ) 10 x x = 5 x 2 x x 35 = 5 x 7 = 5 ( 2x - 7) M May

Factorise 7y + 148z - 129x + 152x - 24 = 7(y + 2)= 4(2z - 3)= 3(3x + 5)= 2(x - 12) 5x + 10x 2 4x x2x 2 + 4x2x 3 - 3x 2 = 5x(1 + 2x)= 2x(2x + 5)= 2x(x + 2)= x 2 (2x - 3) 5.x x.x 2.2.x.x. 5.2.x. 2.x.x 2.2.x 2.x.x.x 3.x.x 14xy + 49y 2 3x x = 7y(2x + 7y)= 3x(x - 4) 8x 2 + 4x = 4x(2x - 1) M May

( x + 4 ) ( x + 7 ) Multiply out the brackets: ( x - 4 ) ( x - 7 ) ( x + 4 ) ( x - 7 )( x - 4 ) ( x + 7 ) = x x + 4 x + 28 = x x + 28 = x x - 4 x + 28 = x x + 28 = x x + 4 x - 28 = x x - 28 = x x - 4 x - 28 = x x - 28 M May

Multiply out these brackets (x + 2) (x + 7)(x - 2) (x + 7)(x + 2) (x - 7) (x - 2) (x - 7)(x - 6) (x - 9)(x - 1) (x + 1) = x x + 2 x + 14 = x x +14 = x x - 2 x - 14 = x x -14 = x x + 2 x - 14 = x x -14 = x x - 2 x + 14 = x x +14 = x x - 6 x + 54 = x x +54 = x 2 + x - x - 1 = x M May

To factorise (putting the brackets back in!) x x + 14 = ( ) ( ) x x 14 = 1 x 14 2 x 7 Add = So = ( x + 2 ) ( x + 7 ) Always check by mutliplying out. x x + 14 = ( x + 2 ) ( x + 7 ) M May

Factorise x x + 2x x + 6x x - 10 x x + 10x 2 + x - 12x x - 12 = ( x + 2)( x +1)= ( x - 2)( x - 3)= ( x - 2)( x + 5) = ( x - 2)( x - 5)= ( x - 3)( x + 4)= ( x - 6)( x + 2) (+) 6 = 1 x 6 2 x = -5 (-) 10 = 1 x 10 2 x = +3 (+) 10 = 1 x 10 2 x = -7 (-) 12 = 1 x 12 2 x 6 3 x = 1 (-) 12 = 1 x 12 2 x 6 3 x = -4 M May