Rekenen met variabelen *: 3.1 Haakjes wegwerken *
Expanding brackets
Distributive Properties The distributive properties of multiplication with respect to addition and subtraction (also called distribution properties) are the following: \[a\cdot (b+c)=a\cdot b+a\cdot c\qquad\mathrm{and}\qquad (a+b)\cdot c=a\cdot c+b\cdot c\]
The properties \[a\cdot (b+c)=a\cdot b+a\cdot c\qquad\mathrm{and}\qquad (a+b)\cdot c=a\cdot c+b\cdot c\] do not only apply if you take numbers for \(a\) and \(b\) and place the omitted multiplication signs correctly, but also when the letters represent algebraic expressions.
You can still formulate distributive properties as \[a\cdot (b- c)=a\cdot b-a\cdot c\qquad\mathrm{and}\qquad (a-b)\cdot c=a\cdot c-b\cdot c\tiny,\] but these properties follow immediately from the former properties by reading \(-c\) and \(-b\) as \({}+(-c)\) and \({}+(-b)\).
The distributive properties can be used to remove brackets. Here are some examples to show how that works.
Apply the distributive properties to: \[6(-s+3)=(6\times -s)+(6\times3)=-6s+18\tiny.\]
You should be careful when you are dealing with minus signs. An example where it is easy to make a mistake is \[-(a^2-a)\tiny.\] Expanding the brackets is a little tricky because the term outside the brackets is difficult to recognize; you have to read the expression as \[-1\cdot(a^2-a)\] and then the brackets can be expanded in the following way: \[ \begin{array}{rcl}-(a^2-a)&=&-1\cdot(a^2-a)\\ &=&-1\cdot a^2\;+\;-1\cdot -a\\ &=&-a^2+a\end {array}\]
Or visit omptest.org if jou are taking an OMPT exam.
