Expansion & Factorisation

Collecting Like Terms

100

Simplify the following:

x²+3x²+2x

4x²+2x

200

Simplify the following:

3t+7-t-11

2t-4

300

Simplify the following:

2cd+dc-4d+3cd

6cd-4d

400

Simplify the following:

3x³-x²+2x²-3x+x³

4x³+x²-3x

500

Simplify the following:

ab²+2ab+a²b

ab²+2ab+a²b

Distributive Law

100

Expand & simplify the following:

8(a-2b)

8a-16b

200

Expand & simplify the following:

-3x(7-4x)

12x²-21x

300

Expand & simplify the following:

6x(x²+5x-2)

6x³+30x²-12x

400

Expand & simplify the following:

6(x-2)-8x

-2x-12

500

Expand & simplify the following:

4(3x-2)-(3x+1)

9x-9

FOIL Expansion

100

Expand & simplify the following:

(x+4)(x+6)

x²+10x+24

200

Expand & simplify the following:

(x+6)(x-6)

x²-36

300

Expand & simplify the following:

(3x+2)(4x+1)

12x²+11x+2

400

Expand & simplify the following:

(x-3)(x+6)+4(x+2)

x²+7x-10

500

Expand & simplify the following:

(x+2)(x-2)+(x+6)²

2x²+12x+32

Difference of two squares

100

Expand to form a difference of two squares:

(x+4)(x-4)

x²-16

200

Expand to form a difference of two squares:

(x+8)(x-8)

x²-64

300

Expand to find the difference of two squares:

(3x+4)(3x-4)

9x²-16

400

Expand to find the difference of two squares:

(5x-7)(5x+7)

25x²-49

500

Expand to find the difference of two squares:

(7x+11)(7x-11)

49x²-121

Factorising

100

Fully factorise the following:

14x+21xy

7x(2+3y)

200

Fully factorise the following:

2a²+8a

2a(a+4)

300

Fully factorise the following:

-3b-12ab

-3(b+4a)

400

Fully factorise the following:

-ab²-a²b

-ab(a+b)

500

Fully factorise the following:

4y²-18y+14xy

2y(2y-9+7x)

Substitution

100

If k=3, j=5 and m=-2, find the value of:

4k+7-3j

4

200

If k=3, j=5 and m=-2, find the value of:

8km-2j

-58

300

If p=4, q=-3, and r=2 evaluate:

(p+r)/q

-2

400

If p=4, q=-3, and r=2 evaluate:

((3p+r))/(p+r-2q

3/2

500

If a=4, b=-1 and c=3, evaluate:

sqrt(8c+2ab)

4