What is 2a times a
Multiply / resolve brackets (also to the power of 2)
How to expand brackets - that is, to resolve them - is what we look at here. This is what you get:
- A Explanationhow to multiply different brackets.
- Lots Examples for breaking brackets.
- tasks / Exercises to practice breaking the brackets yourself.
- Videos to the calculation in brackets.
- A Question and answer area to this topic.
We're looking at how to get rid of parentheses here. If you need a more general overview of the calculation in brackets, please see the main article Calculating with brackets. Otherwise continue to resolve brackets.
Explanation dissolve bracket
There are many ways to deal with and resolve parentheses. So we're going through many of the cases here.
Plus sign in front of bracket:
Let's start very simply: we have a number in front of the brackets - in this case a 5 - and a plus and numbers in the brackets. Here you can easily remove the brackets.
Of course you can also calculate in brackets 8 - 3 = 5 and then 5 + 5 = 10. Of course, this doesn't work if you don't know the numbers. If you don't know these - i.e. have variables (unknowns) - it would look like this:
Factor times bracket:
We have a bracket with numbers in it. In front of this bracket there is a number that is multiplied by the bracket. This is also known as factor times bracket. You solve this by multiplying the factor in front of the brackets by every number in the brackets.
This problem could of course also be solved by adding the numbers in brackets and then multiplying by the 5 in front of it. This is no longer possible if variables - i.e. still unknown numbers - occur:
Minus sign in front of brackets:
A minus sign can also be placed in front of the bracket. In this case you can write this with -1 and treat it like that. As a result, the sign of the elements in the brackets is reversed when they are multiplied out. A few numbers for a better understanding:
Again another example, this time with some unknowns to show this again. Here, too, you have to note that the minus in front of the brackets becomes -1. If you multiply each element in brackets by this -1, all signs are reversed. In the last line a - 3a = - 2a are summarized.
Examples Expand bracket
In this area, further examples for multiplying brackets are to be calculated.
Multiply bracket times bracket:
Let's look at another case of expanding / resolving parentheses. The way it works is that every element of one bracket is multiplied by every element of the other bracket. The correct handling of the terms must of course be observed.
Dissolve parentheses in parentheses:
Of course, this also works with more demanding tasks that involve a mix of numbers and variables. Another small feature: We have brackets in brackets here. How do you solve this? First the inner bracket is calculated, then the outer bracket.
Dissolve brackets with high 2:
Dissolving a bracket with a "high 2" should still be shown here. So we have a power with the exponent number 2. This is nothing more than calculating parentheses times parentheses. Here is another example:
Tasks / exercises Multiply bracketsShow:
Dissolve video brackets
Examples Expand brackets
The next video covers how to use brackets. It is also about multiplying parentheses. In order to explain this simply, many examples are calculated, with and without variables.
Next video »
Questions with answers multiply brackets
This section covers typical questions with answers about expanding parentheses.
Q: In what order do brackets (and powers) have to be calculated?
A: The calculations must be done in this order:
- Point calculation (multiplication and division)
- Line calculation (addition and subtraction)
- Left to right
The priority therefore looks like a parenthesis before a power and then a point calculation before a line calculation. At the end it is calculated from left to right.
Q: When is parenthesis breaking covered in school?
A: Most of the time, the use of brackets is dealt with in 5th grade at the latest. For example, the associative law is dealt with here in order to solve simple tasks with brackets. Then tasks with factors in front of the brackets or several brackets and unknowns are dealt with. This mostly takes place in the 6th grade and 7th grade.
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