Transcript Lesson 8 Expand and Simplify. Mathswatch 103
Lesson 8 Expand and Simplify.
Mathswatch 103
GCSE Maths Starter 8
1) Describe the correlation.
5) Solve the equations below: 2. Write 14 as a percentage of 20 3. What is 3y x 5y ?
4. Convert 2500g to kg
Lesson 8 Expand and Simplify.
Mathswatch 103 • • • To simplify expressions by collecting like terms.
To expand individual single brackets.
To expand and simplify more than one single bracket.
EXTN: To expand and simplify double brackets. (Grade C)
Lesson 8 Expand and Simplify.
Mathswatch 103 By expanding brackets we mean
multiply
each term in the bracket by the term outside. Because it is multiplying, we use the
grid method
for this.
Expand the following expression 3(x - 9)
x - 9 3 3x -27
Final Ans: 3x -27
Expand the following expression
Lesson 8 Expand and Simplify.
Mathswatch 103 x x x² x(x +7) + 7 +7x
Final Ans: x² + 7x
Lesson 8 Expand and Simplify.
Mathswatch 103 Now you try these…… (You have 5 mins max and must show your working) Expand each of the following: (a) 3(
x
+ 8) (b) 7(
x
+ 2) (c) 2(5
x
- 2) (d) 8(2
x
- 3) (e) 7(
y
+ 1) (f) 9(3
k
- 8) (a) 3
x
+ 24 (b) 7
x
+ 14 (c) 10
x
- 4 (d) 16
x
- 24 (e) 7
y
+ 7 (f) 27
k
- 72
Questions 1
Lesson 8 Expand and Simplify.
Mathswatch 103 What happens when we have two individual brackets with a plus or minus between them like below: 5(x - 4) + 3(x- 3)
Answer: We do two separate 2 x 1 grids then collect up like things.
5 x 5x - 20
5x - 20 Final Ans:
- 4 + x 3 3x +
8x - 29 3x - 9
- 3 - 9 Watch out for negatives.
Lesson 8 Expand and Simplify.
Mathswatch 103 Now some for you to try: How many can you do in 5 minutes? (with workings!) Expand and simplify each of the following: (a) 4(
x
+ 5) + 3(
x
+ 2) (b) 2(3
x
+ 1) - (
x
+ 3) (c) 3(5
x
- 2) + 2(
x
- 1) (d)
-
7(
x
- 2) - 2(
x
- 1) (e) 5(3
x
- 1) - 4(2
x
- 3) + 3(
x
+ 4) (f) 9
+
2(5
x
- 3) - 7(2
x
+ 4) + 5
x
(a) 7
x
+ 26 (b) 5
x
- 1 (c) 17
x
- 8 (d) 16 - 9
x
(e) 10
x
+ 19 (f)
x
- 25
Lesson 8 Expand and Simplify.
Mathswatch 103 What’s the difference?
a) 4(x + 6) + 2(x – 7) b) (4x+6)(2x-7)
So how do we expand when we have two brackets right next to each other then?......
Lesson 8 Expand and Simplify.
Mathswatch 103 x Expand and simplify the following expression x x² +5 +5x (x + 5)(x - 6) - 6
- 6x
-30
Final Ans: x²-
x
- 30
Watch out for negatives.
Lesson 8 Expand and Simplify.
Mathswatch 103 2a Expand and simplify the following expression 4a 8a² +3 +12a (2a + 3)(4a + 2) +2 +4a +6
Final Ans: 8a²+
16a
+6
Lesson 8 Expand and Simplify.
Mathswatch 103 Now some for you to try: How many can you do in 5 minutes? (with workings!) Expand and simplify each of the following: Watch out for negatives.
(a) (x + 5)(x + 2) (b) (x - 1)(x + 3) (c) (x - 6)(x + 1) (d) (x - 2)(x - 3) (e) (3x + 1)(2x + 3) (f) (5x - 3)(2x + 4) (a) x² + 5x + 2x + 10 (b) x² -1x +3x -3 (c) x² - 6x +1x -6 (d) x² - 2x – 3x +6 (e) 3x²+2x +9x+3 (f) 10x²-6x+20x-12 (a) x² + 7x +10 (b) x² +2x-3 (c) x² - 5x -6 (d) x² -5x +6 (e) 3x²+11x+3 (f) 10x²+14x-12
Lesson 8 Expand and Simplify.
Mathswatch 103
Lesson 8 Expand and Simplify.
Mathswatch 103 • • • To simplify expressions by collecting like terms.
To expand individual single brackets.
To expand and simplify more than one single bracket.
EXTN: To expand and simplify double brackets. (Grade C)