algebra revision

Factorising

100

x²+x-30

(x-5)(x+6)

200

8p-6q+10r

2(4p-3q+5r)

300

3x²-10x-48

(x-6)(3x+8)

400

1-t⁴

(t²+1)(t+1)(−t+1)

500

120x²+67x−5

(8x+5)(15x−1)

Rearranging formulas

100

m=5x²

x=√m/5

200

a=πx²/9

9a/√π

300

y=³√x/a

x=(ya)³

400

1/x++1/y=1/t

make x the subject

x=t-y/1

500

a=y+t/p+x²

x=√y+t/a-p

Linear equations

100

12=20+2x

x=-4

200

3(p+4)=21

p=3

300

4(x-5)=7(2x-5)

x=1.5

400

7+2x/3=9x-1/7

x=4

500

2x+3/4-4x-2/6

-x/6+13/12

Simultaneous equations

100

2x+2y=16

x-3y=4

x=7

y=1

200

4x + y = 23 

x + y = 8

x=5

y=3

300

2y+3x=6

x=4y+16

x=4

y=-3

400

3x+2y=22

2x+2y=18

y=5

x=4

500

4.4x-4.8y=2.2

0.8+2.4y=4

x=1.7

y=1.1

Quadratics

100

x²-6x-27

(x+3)(x-9)

200

x²-15x+56

3(x-7)(x-8)

300

x²+9x-36

9(x+12)(x-3)

400

x²-18x+45

x = 15, x=3

500

4x²+7x-13

x=1.13, x=-2.88