1 Expand

a 2(x + 1) ................................... b 5(x –1) ...................................

c 3(p – q) ................................... d 4(2 – s) ...................................

2 Expand

a 3(2x + 1) ................................... b 2(5x – 3) ...................................

c 5(n2 – 3n) ................................... d 2(n2 – 3n) ...................................

3 Expand

a x(x – 1) ................................... b x(x + 4) ...................................

c y(3 – y) ................................... d p(p + 5) ...................................

4 Expand

a t(2t + 1) ................................... b y(3y – 2) ...................................

c x(4x + 3) ................................... d a(5 – 2a) ...................................

5 Expand

a −5(x – 1) ................................... b −3(x + 4) ...................................

c −2(3x + 4) ................................... d –x(x + 1) ...................................

6 Expand

a −4(y – 2) ................................... b −2(1 – x) ...................................

c −3m(m – 1) ................................... d −2x(x – 2) ...................................

7 Expand and simplify

a 2(x + 1) + 3x b 3(x + 2) + 4(x – 1)

.................................................................................................... ....................................................................................................

c x(y + 1) + y(x + 1) d x(x – 1) + 2x(x + 3)

.................................................................................................... ....................................................................................................

8 Expand and simplify

a 5(y + 2) – 2(y + 3) b y(y + 5) – y(y + 1)

.................................................................................................... ....................................................................................................

c 2y(y – 3) – 5(y – 1) d 3y(y – 5) – 2y(y – 2)

.................................................................................................... ....................................................................................................

�2 8.1 Expanding brackets

119

Hint Remember to multiply every term inside the bracket.

Hint Watch the signs outside and inside the bracket.

Guided practice worksheet

D

C

Questions are targeted at the grades indicated

1 Factorise

a 2x + 2 ................................. b 6x + 3 ................................. c 5x – 15 ................................. d 3 – 3x .................................

2 Factorise

a 10y + 25 ................................. b 7y – 14 ................................. c pq + qr ................................. d s2 – st .................................

3 Factorise fully

a 12x + 18 ............................................................... b 16x – 24 ...............................................................

c 3ab + 9a ............................................................... d 4x2 + 2x ...............................................................

4 Factorise fully

a 2y + 8y2 ............................................................... b p2q − pq2 ...............................................................

c 27a2 – 18a ............................................................... d 30x2 + 50xy ...............................................................

5 Factorise

a x(x + 1) + x(x + 2) b (x – 1)2 + (x – 1)

.................................................................................................... ....................................................................................................

c 2(x + 3) + (x + 3)2

....................................................................................................

6 Factorise fully

a 3x(x + 1) + 6x(x + 2) b 5(x – 2)2 – 10(x – 2)

.................................................................................................... ....................................................................................................

c 4(3x + 1)2 – 2(3x + 1)

....................................................................................................

�2 8.2 Factorising by taking out common factors

121

Guided practice worksheet

D

C

B

Questions are targeted at the grades indicated

�2 8.3 Expanding the product of two brackets

123A

Expand and simplify the following brackets

1 (x + 4) (x + 5)

..................................................................................

3 (x + 3) (x + 6)

..................................................................................

5 (x + 3) (x – 2)

..................................................................................

7 (x – 1) (x + 3)

..................................................................................

9 (x – 3) (x – 4)

..................................................................................

1 1 (x + 4)2

..................................................................................

2 (x + 2) (x + 8)

..................................................................................

4 (x + 1) (x + 9)

..................................................................................

6 (x + 5) (x – 5)

..................................................................................

8 (x – 4) (x + 2)

..................................................................................

1 0 (x – 5) (x – 6)

..................................................................................

1 2 (x – 6)2

..................................................................................

Hint Multiply every term inside the bracket by every term outside the bracket.

Guided practice worksheet

B

Questions are targeted at the grades indicated

�2 8.3 Expanding the product of two brackets

123B

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

..................................................................................

1 5 (x – 1) (2x + 1)

..................................................................................

1 7 (x – 3) (3x – 1)

..................................................................................

1 9 (2x – 5)2

..................................................................................

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

..................................................................................

1 6 (4x + 5) (x – 2)

..................................................................................

1 8 (2x + 5)2

..................................................................................

2 0 (3x + y)2

..................................................................................

Guided practice worksheet

A

�2 8.4 Factorising quadratic expressions

125A

1 a Write down a pair of numbers whose product is +2 and whose sum is +3.

..................................................................................................

b Factorise x2 + 3x + 2. ..................................................................................................

2 a Write down a pair of numbers whose product is −3 and whose sum is +2.

..................................................................................................

b Factorise x2 + 2x – 3. ..................................................................................................

3 a Write down a pair of numbers whose product is +7 and whose sum is −8.

..................................................................................................

b Factorise x2 – 8x + 7 ..................................................................................................

4 Factorise

a x2 + 6x + 5 b x2 + 10x + 21

...................................................................................................... ......................................................................................................

5 Factorise

a x2 + 5x – 24 b x2 – x – 20

...................................................................................................... ......................................................................................................

6 Factorise

a x2 – 9x + 8 b x2 – 18x + 81

...................................................................................................... ......................................................................................................

7 Use the difference of two squares to factorise

a x2 – 16 b x2 – 121 c 25 − x2

............................................ ............................................ ............................................

Guided practice worksheet

B

A2 − B2 = (A + B) (A –B)

Questions are targeted at the grades indicated

A

�2 8.4 Factorising quadratic expressions

125B

Guided practice worksheet

8 Complete the following

a 2x2 +5x + 2 = (2x + 1) (.............................................)

b 6x2 + 5x – 4 = (3x + 4) (.............................................)

c 4x2 – 9x + 2 = (4x – 1) (.............................................)

9 Factorise 5x2 + 31x + 6

..................................................................................................

1 0 Factorise 6x2 – 5x – 25

..................................................................................................

A