QUICK COVER
Expanding and Simplifying 1
Task 1 : Collecting like terms : 3x + 4 + 5x + 2 (all positive)
Task 2 : Expand a single bracket : 4(3x + 5) (all positive)
Task 3 : Expand a single bracket and collect like terms : 5(2x + 1) + 3x + 2 (all positive)
Task 4 : Expand 2 brackets and collect like terms : 4(2x + 3)+2(4x + 1) (all positive)
Puzzle : Expand 2 brackets and collect like terms : 4(2x + 3)+2(4x + 1) (all positive)
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Help and hints……
TASK 1
Example
TASK 2
Simplify
Example
2x + 3 + 4x + 2
TASKS 3 Expand and simplify
Expand
5(3x + 4)
= 5 × 3x + 5 × 4
= 2x + 3 + 4x + 2
= 2x + 4x
Expanding and Simplifying 1
= 15x + 20
+ 3 + 2
= 6x + 5
Example
3(2x + 5) + x + 4
= 6x + 15 + x + 4
= 7x + 19
‘Expand’ means
‘Multiply out’
You cannot ‘mix’ your
Expand the
TASK 4
bracket(s) first
Example
x’s and numbers
2(3x + 1) + 3(x + 5)
You can use a grid to expand the brackets
5(3x + 4)
×
3x
5
15x
+4
+20 = 15x + 20
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= 6x + 2 + 3x + 15
= 9x + 17
Expanding and Simplifying 1
TASK 1
Simplify
TASK 2
Expand
TASK 3
Expand and
simplify
TASK 4
Expand and
simplify
1. 8x + 5 + 3x + 6
1. 8(9x + 5)
1. 3(3x + 5) + 4x + 3
1. 2(5x + 2) + 3(3x + 2)
2. 7x + 5 + 7x + 4
2. 8(8x + 5)
2. 2(4x + 1) + 2x + 2
2. 2(4x + 5) + 4(4x + 1)
3. 10x + 5 + 6x + 4
3. 4(9x + 7)
3. 2(4x + 1) + 5x + 3
3. 4(4x + 7) + 4(4x + 1)
4. 6x + 5 + 5x + 7
4. 6(7x + 3)
4. 3(2x + 5) + 3x + 2
4. 4(2x + 7) + 2(3x + 5)
5. 7x + 3 + 8x + 8
5. 2(9x + 5)
5. 2(5x + 4) + 3x + 3
5. 2(3x + 4) + 4(4x + 5)
6. 5x + 2 + 7x + 5
6. 7(4x + 3)
6. 3(2x + 1) + 4x + 2
6. 3(3x + 5) + 5(5x + 4)
7. 5x + 3 + 6x + 5
7. 2(3x + 7)
7. 3(4x + 3) + 5x + 4
7. 3(5x + 3) + 4(3x + 4)
8. 7x + 4 + 4x + 6
8. 5(5x + 7)
8. 5(3x + 4) + 2x + 5
8. 2(5x + 1) + 4(4x + 1)
9. 9x + 3 + 5x + 7
9. 9(2x + 11)
9. 3(5x + 1) + 5x + 2
9. 3(4x + 7) + 4(3x + 5)
10. 8x + 3 + 8x + 3
10. 6(9x + 5)
10. 4(3x + 2) + 3x + 2
10. 4(4x + 1) + 3(4x + 1)
11. 9x + 5 + 3x + 6
11. 4(8x + 11)
11. 3(5x + 7) + 2x + 3
11. 5(2x + 7) + 5(4x + 1)
12. 10x + 3 + 3x + 5
12. 2(5x + 2)
12. 5(4x + 1) + 5x + 2
12. 4(3x + 5) + 2(3x + 2)
13. 8x + 2 + 7x + 4
13. 10(7x + 11)
13. 4(5x + 4) + 4x + 2
13. 2(2x + 3) + 4(3x + 4)
14. 6x + 2 + 5x + 7
14. 3(8x + 3)
14. 3(4x + 5) + 3x + 4
14. 5(5x + 1) + 3(5x + 1)
15. 8x + 4 + 5x + 7
15. 8(3x + 4)
15. 5(5x + 3) + 4x + 2
15. 5(5x + 3) + 5(2x + 7)
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Expanding and Simplifying 1
ANSWERS
TASK 1
TASK 2
TASK 3
TASK 4
1.
11x + 11
1.
72x + 40
1.
13x + 18
1.
19x + 10
2.
14x + 9
2.
64x + 40
2.
10x + 4
2.
24x + 14
3.
16x + 9
3.
36x + 28
3.
13x + 5
3.
32x + 32
4.
11x + 12
4.
42x + 18
4.
9x + 17
4.
14x + 38
5.
15x + 11
5.
18x + 10
5.
13x + 11
5.
22x + 28
6.
12x + 7
6.
28x + 21
6.
10x + 5
6.
34x + 35
7.
11x + 8
7.
6x + 14
7.
17x + 13
7.
27x + 25
8.
11x + 10
8.
25x + 35
8.
17x + 25
8.
26x + 6
9.
14x + 10
9.
18x + 99
9.
20x + 5
9.
24x + 41
10.
16x + 6
10.
54x + 30
10.
15x + 10
10.
28x + 7
11.
12x + 11
11.
32x + 44
11.
17x + 24
11.
30x + 40
12.
13x + 8
12.
10x + 4
12.
25x + 7
12.
18x + 24
13.
15x + 6
13.
70x + 110
13.
24x + 18
13.
16x + 22
14.
11x + 9
14.
24x + 9
14.
15x + 19
14.
40x + 8
15.
13x + 11
15.
24x + 32
15.
29x + 17
15.
35x + 50
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3(5x + 3) + 3(3x + 2)
3(5x + 3) + 5(5x + 2)
16x + 38
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3(3x + 5) + 3(3x + 5)
27x + 13
30x + 63
4(2x + 5) + 2(5x + 2)
23x + 19
2(3x + 7) + 3(2x + 7)
28x + 20
5(3x + 5) + 2(3x + 5)
3(5x + 3) + 4(3x + 1)
4(4x + 1) + 4(3x + 2)
28x + 39
40x + 19
4(4x + 7) + 5(5x + 3)
21x + 36
4(4x + 1) + 4(3x + 4)
16x + 17
4(4x + 1) + 2(2x + 7)
2(2x + 5) + 4(3x + 4)
21x + 35
4(2x + 7) + 2(4x + 5)
14x + 49
24x + 40
18x + 30
4(3x + 1) + 3(5x + 2)
5(4x + 1) + 5(3x + 5)
24x + 15
5(2x + 7) + 4(5x + 7)
3(4x + 7) + 3(5x + 2)
5(3x + 4) + 5(5x + 1)
27x + 10
4(3x + 7) + 5(2x + 3)
16x + 26
2(2x + 7) + 5(2x + 7)
20x + 18
28x + 12
22x + 43
18x + 24
3(3x + 7) + 4(4x + 1)
40x + 25
3(3x + 5) + 3(4x + 7)
2(3x + 1) + 5(5x + 2)
5(4x + 5) + 4(3x + 4)
27x + 27
3(2x + 3) + 2(5x + 4)
4(2x + 7) + 4(4x + 3)
12x + 35
2(4x + 5) + 3(5x + 3)
35x + 30
41x + 43
5(4x + 7) + 4(2x + 1)
25x + 25
31x + 12
32x + 41