algebraic factorising

HCF

100

2x-2

2(x-1) 

200

A²+A

A(A+1)

300

8ab-20ac

4a(2b-5c) 

400

-12b²+22b

2b(-6b+11)

500

-6px+15xy

3x(-2p +5y) 

Quadratics

100

x²+3x+2

(X+1)(x+2)

200

x²-10x+21

(x-3)(x-7)

300

q²-4q+4

(q-2)(q-2) 

or 

(q-2)²

400

7x²+9x+2

(7x+2) (x+1)

500

1/4 x²+3x+5

(X+2)(x+10)

Grouping

100

px+py+qx+qy 

(p+q)(x+y)

200

wx-wy+5x-5y

(W+5)(x-y)

300

6xy-3ay+10bx-5ab

(3y+5b)(2x-a)

400

wy-y-1+w

(y+1)(w-1)

500

2x²-3xy+2ax-3ay

(2x-3y) (x+a)

Difference of two squares

100

x²-25

(x-5)(x+5)

200

y²-144

(y-12)(y+12)

300

25x²-81

(5x-9)(5x+9)

400

144m²-25n²

(12m-5n)(12m+5n)

500

36a⁴b²-49c⁶

(6a²b-7c³)(6a²b+7c³)

Random

100

2x² -6x

(2x)(x-3)

200

9a⁴ -25b²

(3a²-5b)(3a²+5b)

300

6x²-5x-6

(2x-3)(3x+2)

400

2ax+6ay+bx+3by

(2a+b)(x+3y)

500

8m³n-18mn

2mn(4m²-9)

2m[ (2m-3) (2m+3)]