### Lesson 8 Expand and Simplify. Mathswatch 103

```Lesson 8 Expand and Simplify.
Mathswatch 103
GCSE Maths Starter 8
1) Describe the correlation.
2. Write 14 as a percentage of 20
3. What is 3y x 5y ?
4. Convert 2500g to kg
5) Solve the equations
below:
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.
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)
3
Final Ans:
x
-9
3x
-27
3x -27
Lesson 8 Expand and Simplify.
Mathswatch 103
x
Expand the following
expression
x
x²
x(x +7)
Final Ans: x² + 7x
+7
+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(5x - 2)
(d) 8(2x - 3)
(e) 7(y + 1)
(f) 9(3k - 8)
(a) 3x + 24
(b) 7x + 14
(c) 10x - 4
(d) 16x - 24
(e) 7y + 7
(f) 27k - 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
5x
-4
- 20
+
+
x
3
x
-3
3x
-9
5x - 20
3x - 9
Final Ans: 8x - 29
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(3x + 1) - (x + 3)
(c) 3(5x - 2) + 2(x - 1)
(d) -7(x - 2) - 2(x - 1)
(e) 5(3x - 1) - 4(2x - 3) + 3(x + 4)
(f) 9 + 2(5x - 3) - 7(2x + 4) + 5x
(a) 7x + 26
(b) 5x - 1
(c) 17x - 8
(d) 16 - 9x
(e) 10x + 19
(f) x - 25
Lesson 8 Expand and Simplify.
Mathswatch 103
What’s the difference?
a)
b)
4(x + 6) + 2(x – 7)
(4x+6)(2x-7)
So how do we expand when we have two
brackets right next to each other
then?......
Answer: Just the same but a 2 x 2 grid.
Questions 1
Lesson 8 Expand and Simplify.
Mathswatch 103
Expand and simplify
the following
expression
(x + 5)(x - 6)
x
x
-6
x²
- 6x
Final Ans: x²-- x - 30
+5
+5x
-30
Watch out
for
negatives.
Lesson 8 Expand and Simplify.
Mathswatch 103
Expand and simplify
the following
expression
(2a + 3)(4a + 2)
2a
+3
4a
8a²
+12a
+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)
(a) x² + 5x + 2x + 10
(a) x² + 7x +10
(b) (x - 1)(x + 3)
(b) x² -1x +3x -3
(b) x² +2x-3
(c) (x - 6)(x + 1)
(c) x² - 6x +1x -6
(c) x² - 5x -6
(d) (x - 2)(x - 3)
(d) x² - 2x – 3x +6
(d) x² -5x +6
(e) (3x + 1)(2x + 3)
(e) 3x²+2x +9x+3
(e) 3x²+11x+3
(f) (5x - 3)(2x + 4)
(f) 10x²-6x+20x-12
(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.