Year 10 - Expanding and Factorising

Working with Algebraic Terms

100

If a = 1, b = 3, and c = -2, evaluate 

ac-2bc

10

200

Simplify 

k - 3m + 5m + 7k

8k+2m

300

Simplify 

x + 4x^2 - 8x + 1 + 5x - x^2

3x^2 - 2x + 1

400

Simplify 

4c^2d * abc * 3d

12abc^3d^2

500

Simplify 

(10a^2bc)/(-5abc^2d)

(-2a)/(cd)

Expanding Algebraic Expressions

100

Expand 

2(6-c)

12-2c

200

Expand 

(x+2)(x+5)

x^2 +7x + 10

300

Expand 

(m+8)(m-8)

m^2 - 64

400

Expand 

(x + 3)^2

x^2 +6x + 9

500

Expand and simplify 

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

6a^2+14a-6

Factorising Algebraic Expressions

100

Factorise 

12d + 8

4(3d + 2)

200

Factorise

-4k - 8k^2

-4k(1 + 2k)

300

Factorise 

25-49p^2

(5 + 7p)(5 - 7p)

400

Factorise 

m^2 + 8m + 16

(m + 4)^2

500

Factorise 

m(k-2)+4(k-2)

(k-2)(m+4)

Factorising Quadratic Trinomials

100

Factorise 

x^2 + 10x + 16

(x + 2)(x+8)

200

Factorise 

3x^2 + 15x + 18

3(x+3)(x+2)

300

Factorise 

x^2 + 16x + 64

(x+8)^2

400

Factorise 

x^2 - 12x + 36

(x + 6)(x - 6)

500

Factorise 

x^2+6x+9

(x+3)^2

Working with Algebraic Fractions

100

Simplify 

(2(x+3))/10

(x+3)/5

200

Simplify 

((x+7)(x+2))/((x-8)(x+7))

(x+2)/(x-8)

300

Simplify 

(x-3)/x*(5x)/(x-3)

5

400

Simplify 

(6x)/(x-5)/(2x)/(x-5)

3

500

Simplify 

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

(x+10)/12