Algebra Basics III

Having looked at addition & subtraction of algebraic expressions. Let’s move onto multiplication & division. Let’s start off using the skills we learned in primary school.

Consider this:    What is  5\times(2+3)   equal to?

Easy enough right?  25 . Well, how did we get that answer? You probably did something like this:

5\times(2+3) = 5\times(5) = 25

Here we calculated what was inside the brackets first. You’ve been told to do this ever since you learned BIDMAS (or BODMAS).

Recall: ‘BIDMAS’ is an acronym which reminds us which order we apply operations; Brackets, Indices, Division, Multiplication, Addition, Subtraction.

However this doesn’t always apply. For the above example, we can first multiply 2, and 3, by 5, before adding them together (calculating inside the brackets) like so:

5\times(2+3) = (5\times 2 + 5\times 3) = (10+15) = 25

Notice how the 5 merges into the brackets

Side note: This act of merging (multiplying) into the brackets
only ever works if the brackets are not raised to any number, but 1.
5\times(2+3)^2\neq (5\times2+5\times3)^2 
*Check with a calculator.

Now let’s apply that same ‘merging’ to algebraic expressions.

Consider this:    Expand  5\times(a+b)   .

5\times(a+b) = 5\times a + 5\times b

Recall: In algebra we usually ‘drop’ the multiplication sign. This is done to make things look neater, and to avoid confusion between the symbols x and \times . To indicate multiplication between things, we just place the two together.

Consider this:    Expand  5\times(a+b)   .

5\times(a+b) = 5(a+b) = 5a + 5b

All you really need to remember is too multiply everything in the brackets by what is outside of the brackets. A few more examples:

Expand  6(x+2)  .

6(x+2) = 6x+12

Expand  10(3y+2)  .

10(3y+2) =30y+20

Expand  -2(9+z)  .

-2(9+z) = -18-2z

To be continued…

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