Be able to expand brackets and simplify the expressions that arise Objective Be able to expand brackets and simplify the expressions that arise

Question Expand and simplify the following expression (2a + 3)(4a + 2)

Step 1 Multiply the individuals components together (2a + 3)(4a + 2) 2a +3 4a +2

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 2a +3 4a 8a2 +12a +2 +4a +6 Now collect the like terms 16a

Step 3 2a +3 4a 8a2 +12a +2 +4a +6 So we have 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 Multiply the individuals components together (3b + 2)(4b – 6) 3b +2 4b -6

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 2a +3 4a 12b2 +8b +2 -18b -12 Now collect the like terms -10b

Step 3 2a +3 4a 12b2 +8b +2 -18b -12 So we have 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: (2a + 7)(6a + 2) (4b + 5)(3b +9) (5c + 4)(8c – 2) (7d + 5)(3d – 4) (9y –2)(3y + 6) (4p – 3)(2p – 6) (8m – 2)(7m – 4)

Let’s check some answers Time is up! Let’s check some answers

Did you get them correct? (2a + 7)(6a + 2) (4b + 5)(3b +4) (5c + 4)(8c – 2) (7d + 5)(3d – 4) (9y –2)(3y + 4) (4p – 3)(2p – 6) (8m – 2)(7m – 4) 12a2 + 46a +14 12b2 + 31b +20 40c2 +22c - 8 21d2 – 13d -20 27y2 +30y - 8 8p2 –30p + 18 56m2 – 46m +8

Be able to expand brackets and simplify the expressions that arise THINK! Did you meet the objective of the lesson? Be able to expand brackets and simplify the expressions that arise