Quadratics Recap 1

Expanding Brackets

100

Expand and simplify (x+4)(x-2)

x²+2x-8

200

expand and simplify (3x+5)(x-2)

3x²-x-10

300

expand and simplify (5x-5)²

25x²-50x+25

400

expand and simplify (ax+b)(ax+c)

a²x²+abx+acx+bc

or

a²x²+(ab+ac)x+bc

500

Expand and simplify(x+1)(x+2)(x+3)

x³+6x²+11x+6

Fractorising Quadratics

100

factorise x²+7x+12

(x+3)(x+4)

200

factorise x²-9x+14

(x-2)(x-7)

300

factorise 3x²+9x+6

3(x+2)(x+1)

400

factorise x²-x-20

(x+4)(x-5)

500

factorise x²+2.5x+1

(x+0.5)(x+2)

DOPS

100

Expand (x+3)(x-3)

x²-9

200

factorise x²-16

(x+4)(x-4)

300

Factorise x²-7

(x+root7)(x-root7)

400

factorise 9x²-25

(3x+5)(3x-5)

500

Factorise (x+2)²-5

(x+2+root5)(x+2-root5)

Solving Quadratics

100

solve (x+1)(x+2)=0

x=-1, -2

200

solve x²+5x+4=0

x=-1, -4

300

solve (2x+5)(3x-7)=0

x=-5/2 and x=7/3

400

solve (x²+12)/x = -8

x²-8x+12=0

(x-6)(x-2)

x=2, 6

500

solve (x-2)/3 =5/x

x²-2x-15=0

(x-5)(x+3)

x=5, -3

Other

100

factorise x(a+1)+2(a+1)

(x+2)(a+1)

200

expand and simplify (-x-2)(3x-1)

-3x²-5x+2

300

solve x(x-a)=0

x=0, x=a

400

factorise 2bx + 4b - 6x - 12

2b(x+4)-3(x+4)

=(2b-3)(x+4)

500

Find the length and width of a rectangle with area of 24 cm where the length is 5cm more than the width. 

Let L=W+5. Solve W(W+5)=24. 

8cm x 3 cm