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Math Lesson 6.2.5 - How to expand two Expressions inside Brackets Multiplied together
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Welcome to our Math lesson on How to expand two Expressions inside Brackets Multiplied together, this is the fifth 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 two Expressions inside Brackets Multiplied Together
If we have an algebraic expression of the type
we can consider take each element of the first expression separately and apply the expanding property explained in the previous paragraph. This is true for all positive-negative combinations, despite the fact that we have only the 'plus' symbol to illustrate the property. Just be careful to apply the afore-mentioned sign rules.
Hence, we obtain
= a ∙ (c + d) + b ∙ (c + d)
= a ∙ c + a ∙ d + b ∙ c + b ∙ d
Thus, basically each term of the first pair of brackets is multiplied by all terms of the second pair of brackets.
The method above is known as the 'FOIL' method - an acronym for First - Outside - Inside - Last, which means that initially we multiply the first terms in each bracket, then the outside terms, then the inside ones and finally the last terms.
Example 5
Simplify
Solution 5
Let's write the two main parts of the expression inside brackets to separate them from each other. This is because there is a negative sign before the second set of brackets that may lead to confusion.
= [2a ∙ a + 2a ∙ (-2b) - 3b ∙ a - 3b ∙ (-2b)] - [3a ∙ 2a + 3a ∙ (-5b) + b ∙ 2a + b ∙ (-5b)]
= [2a2 - 4ab - 3ab + 6b2 ] - [6a2 - 15ab + 2ab - 5b2 ]
= [2a2 - 7ab + 6b2 ] - [6a2 - 13ab - 5b2 ]
Now we can remove the brackets by observing the sign rules. Thus,
= 2a2 - 7ab + 6b2 - 6a2 + 13ab + 5b2
= -4a2 + 6ab + 11b2
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- Inside Bracket Feedback. Helps other - Leave a rating for this inside bracket (see below)
- Expressions Math tutorial: Expanding Brackets. Read the Expanding Brackets math tutorial and build your math knowledge of Expressions
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- Check your calculations for Expressions questions with our excellent Expressions calculators which contain full equations and calculations clearly displayed line by line. See the Expressions Calculators by iCalculator™ below.
- Continuing learning expressions - read our next math tutorial: Special Algebraic Identities Obtained through Expanding
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