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Welcome to our Math lesson on How to expand three or more Expressions inside Brackets Multiplied together, this is the sixth lesson of our suite of math lessons covering the topic of Expanding Brackets, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Expanding three or more Expressions inside Brackets Multiplied Together
Even when there are more than two brackets involved the approach does not change; the solution simply involves more steps. Thus,
(a + b) ∙ (c + d) ∙ (e + f)
= a ∙ (c + d) ∙ (e + f) + b ∙ (c + d) ∙ (e + f)
= a ∙ (ce + cf + de + df) + b ∙ (ce + cf + de + df)
= ace + acf + ade + adf + bce + bcf + bde + bdf
It is clear that not all these letters represent different variables; some of them may represent just numbers or terms containing a single variable, as in the following example. This helps us obtain a shorter algebraic expression to that shown above.
Example 6
Expand and then simplify the following algebraic expression.
(3x - 1) ∙ (2x + 5) ∙ (x - 2)
Solution 6
Applying the rule of three brackets expansion, yields
(3x - 1) ∙ (2x + 5) ∙ (x - 2)
= 3x ∙ (2x + 5) ∙ (x - 2) - 1 ∙ (2x + 5) ∙ (x - 2)
= 3x ∙ [2x ∙ x + 2x ∙ (-2) + 5 ∙ x + 5 ∙ (-2)] - 1 ∙ [2x ∙ x + 2x ∙ (-2) + 5 ∙ x + 5 ∙ (-2)]
= 3x ∙ [2x2 - 4x + 5x - 10] - 1 ∙ [2x2 - 4x + 5x - 10]
= 3x ∙ [2x2 + x - 10] - 1 ∙ [2x2 + x - 10]
= 3x ∙ 2x2 + 3x ∙ x + 3x ∙ (-10) - 1 ∙ 2x2 - 1 ∙ x - 1 ∙ (-10)
= 6x3 + 3x2 - 30x - 2x2 - x + 10
= 6x3 + x2 - 31x + 10
More Expanding Brackets Lessons and Learning Resources
Expressions Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 6.2 | Expanding Brackets | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 6.2.1 | How to remove the brackets from an Algebraic Expression when no Operations are involved | | |
| 6.2.2 | How to expand brackets when a number multiplies the Expression inside them | | |
| 6.2.3 | How to expand brackets when the Expression inside them Divides a Number | | |
| 6.2.4 | How to expand brackets when a Number Divides an Expression inside them | | |
| 6.2.5 | How to expand two Expressions inside Brackets Multiplied together | | |
| 6.2.6 | How to expand three or more Expressions inside Brackets Multiplied together | | |
| 6.2.7 | Expanding Brackets Summary | | |
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- Expressions Revision Notes: Expanding Brackets. Print the notes so you can revise the key points covered in the math tutorial for Expanding Brackets
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- Continuing learning expressions - read our next math tutorial: Special Algebraic Identities Obtained through Expanding
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