Download Expanding triple brackets

Expanding triple brackets
To expand triple brackets, you need to expand a pair of brackets first to create a 'new' bracket
and then expand the third bracket with your 'new' bracket. It doesn't matter which pair of
brackets you start with.
(x + 1)
(x + 2) (x + 3)
(x + 1)
(x2 + 2x + 3x + 6)
(x + 1)
3
2
2
(x + 5x + 6)
x
+3
x
+ x2
+3x
+2
+2x
+6
x2 + 5x + 6
OR
x2
+ 5x
+6
x
+ x3
+ 5x2
+ 6x
+1
+ x2
+ 5x
+6
2
(x + x + 5x + 5x + 6x + 6)
(x3 + 6x2 + 11x + 6)
x3 + 6x2 + 11x + 6
Top Tips
1. Be neat and lay out your work carefully.
2. Watch out for negative numbers.
Rewrite these without the brackets:
1. (x +1)(x +3)(x +4)
2. (x +2)(x +3)(x +5)
3. (x +1)3
4. (x -2)(x +3)(x +4)
5. (x -1)(x +2)2
6. (x -1)(2x +3)(2x -3)
7. (x +2)(x +3)(2x -1)
8. (2x -1)(x +5)(x -3)
9. (x +2)3
10. (2x +6)(2x -4)(3x -10)
Extension work 1
A graph can be drawn from the expressions you have worked out.
Sketch a couple of your answers and report on what shape the graph is.
Extension work 2
Work out the area of this triangle.
Your answer will be an expression.
(2x - 4)
(3x + 5)
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Expanding triple brackets
Answers
1.
(x +1)(x +3)(x +4)
x 3 + 8x 2 + 19x + 12
2.
(x +2)(x +3)(x +5)
x3 + 10x 2 + 31x + 30
3.
(x +1)3
x3 + 3 x2 + 3x + 1
4.
(x -2)(x +3)(x +4)
x3 + 5x2 - 2x - 24
5.
(x -1)(x +2)2
x3 + 3x2 - 4
6.
(x -1)(2x +3)(2x -3)
4x3 - 4x2 - 9x + 9
7.
(x +2)(x +3)(2x -1)
2x3 + 9x2 + 7x - 6
8.
(2x -1)(x +5)(x -3)
2x3 + 3x2 - 32 x + 15
9.
(x +2)3
x3 + 6x2 + 12x + 8
10. (2x +6)(2x -4)(3x -10)
12x3 - 28x2 - 112x +240
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26779
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