expanding two brackets
TRANSCRIPT
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