1. 3 ( x + 2 ) = 3 x + 6 2 ( 3 x - 5 ) = 6x - 10 xxx - 5 M May

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

3. Factorise 7y + 148z - 129x + 152x - 24 = 7(y + 2)= 4(2z - 3)= 3(3x + 5)= 2(x - 12) 5x + 10x 2 4x 2 + 10x2x 2 + 4x2x 3 - 3x 2 = 5x(1 + 2x)= 2x(2x + 5)= 2x(x + 2)= x 2 (2x - 3) 5.x.1 2.5.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 2 - 12x = 7y(2x + 7y)= 3x(x - 4) 8x 2 + 4x = 4x(2x - 1) M May

4. ( x + 4 ) ( x + 7 ) Multiply out the brackets: ( x - 4 ) ( x - 7 ) ( x + 4 ) ( x - 7 )( x - 4 ) ( x + 7 ) = x 2 + 7 x + 4 x + 28 = x 2 + 11 x + 28 = x 2 - 7 x - 4 x + 28 = x 2 - 11 x + 28 = x 2 - 7 x + 4 x - 28 = x 2 - 3 x - 28 = x 2 + 7 x - 4 x - 28 = x 2 + 3 x - 28 M May

5. 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 2 + 7 x + 2 x + 14 = x 2 + 9 x +14 = x 2 + 7 x - 2 x - 14 = x 2 + 5 x -14 = x 2 - 7 x + 2 x - 14 = x 2 + 5 x -14 = x 2 - 7 x - 2 x + 14 = x 2 - 9 x +14 = x 2 - 9 x - 6 x + 54 = x 2 - 15 x +54 = x 2 + x - x - 1 = x 2 - 1 M May

6. To factorise (putting the brackets back in!) x 2 + 9 x + 14 = ( ) ( ) x x 14 = 1 x 14 2 x 7 Add + 2 + 7 = +9 +2 +7 So = ( x + 2 ) ( x + 7 ) Always check by mutliplying out. x 2 + 9 x + 14 = ( x + 2 ) ( x + 7 ) M May

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