Objective

Be able to expand brackets and simplify the expressions that

arise

Question (Level 6)

• Expand and simplify the following expression

(2a + 3)(4a + 2)

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

2a +3

4a

+2

Multiply the individuals components together

2a +3

4a 8a2

+2

2a +3

4a 8a2 +12a

+2

2a +3

4a 8a2 +12a

+2 +4a

2a +3

4a 8a2 +12a

+2 +4a +6

Step 2

• Now collect the like terms

2a +3

4a 8a2 +12a

+2 +4a +6

16a

Step 3

So we have

2a +3

4a 8a2 +12a

+2 +4a +6

8a2 + 16a + 6

This will always work!

You may have to deal with negatives too,

but don’t worry it’s just as easy.

Dealing with negatives

Expand and simplify the following expression

(3b + 2)(4b – 6)

Step 1(3b + 2)(4b – 6)

3b +2

4b

-6

Multiply the individuals components together

3b +2

4b 12b2

-6

3b +2

4b 12b2 +8b

-6

3b +2

4b 12b2 +8b

-6 -18b

3b +2

4b 12b2 +8b

-6 -18b -12

Step 2

• Now collect the like terms

2a +3

4a 12b2 +8b

+2 -18b -12

-10b

Step 3

So we have

2a +3

4a 12b2 +8b

+2 -18b -12

12b2 –10b – 12

That’s it!

Just be careful when you are multiplying negative numbers and take your time when collecting like

terms.

Let’s try some questions – You only have five minutes!

• Expand and simplify:1) (2a + 7)(6a + 2)2) (4b + 5)(3b +9)3) (5c + 4)(8c – 2)4) (7d + 5)(3d – 4)5) (9y –2)(3y + 6)6) (4p – 3)(2p – 6)7) (8m – 2)(7m – 4)

Time is up!

Let’s check some answers

Did you get them correct?

1) (2a + 7)(6a + 2)

2) (4b + 5)(3b +4)

3) (5c + 4)(8c – 2)

4) (7d + 5)(3d – 4)

5) (9y –2)(3y + 4)

6) (4p – 3)(2p – 6)

7) (8m – 2)(7m – 4)

12a2 + 46a +14

12b2 + 31b +20

40c2 +22c - 821d2 – 13d -20

27y2 +30y - 88p2 –30p + 18

56m2 – 46m +8

THINK!

Did you meet the objective of the lesson?

Be able to expand brackets and simplify the expressions that

arise