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 (Expanding brackets)

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

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

Factorising By HCF

100

Fully factorise the following:

3x+6

3(x+2)

200

Fully factorise the following:

-7a-21a²

-7a(1+3a)

300

Fully factorise the following:

4x²-8x+12

4(x²-2x+3)

400

Fully factorise the following:

9x²-45x-27x³

9x(x-5-3x²)

500

Fully factorise the following:

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

(x-3)(x-4)

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

Riddles

100

Stephen was looking at a photo. Someone asked him: "Whose picture are you looking at?" He replied: "I don't have any brothers or sisters, but this man's father is my father's son". Whose picture was Stephen looking at?

His son.

200

There are several books on a bookshelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?

9 books

300

John has been hired to paint the numbers 1 through 100 on 100 apartments.
How many times with he have to paint 8?

20 times

400

Mr. Smith has 4 daughters. Each of his daughters has a brother.
How many children does Mr. Smith have?

5 children

500

A grandfather, two fathers and two sons went to the movie theater together and everyone bought one movie ticket each. How many tickets did they buy in total?

3