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Mr F’s Maths Notes
Algebra
2. Single Brackets
2. Single Brackets
Once Upon A Time…
I once heard someone explaining a very nice way of thinking about brackets.
He said to think of the brackets as a canoe, and to think of the term outside them as a wave.
Now, as you know, when you are in a canoe, there is no place to hide from the wave, and the
person at the back gets just as wet as the person at the front and those in the middle.
Which brings us nicely onto the single most important rule of brackets…
Key Rule: you must multiply EVERYTHING inside the bracket by the term on the
outside
And so long as you remember this, as well as your Rules of Algebra and how to deal with
Negative Numbers, then this topic should hold no fear for you!
I am going to take you through 4 pretty easy examples to make sure your knowledge of negative
numbers and the rules of algebra is up to scratch, and then it’s time for a few stinkers!
Example 1
Example 2
3(2a  6)
5(7 d  4)
Okay, so remember, the 3 is multiplying the
2a AND the +6.
Sometimes drawing on arrows helps you
remember this, and a box is useful too…
3 (2a  6)
Okay, so remember, the 5 is multiplying the
7a AND the -4.
Let’s get those arrows going again, and a box
too to remind us that the 2nd term in the
bracket is a –4
5 (7d  4)
And so we get…
And so we get…
3  2a  6a
3  6  12
5  7d  35d
5   4   20
a positive x
a negative
Now, we are close to our answer, but we
are missing… a SIGN
And now we have our answer, but notice again
how important it was to get the sign correct.
You must remember your rules for
multiplying with negative numbers
If I had £1 for each time I have seen
35d + 20, or just 35d 20 for questions like
this, I would be loaded!
The 3 and the front is really +3, and the
second term in the bracket is +6, and two
positives multiplied together give a
POSITIVE so…
3(2a  6)  6a  12
Anyway, the correct answer…
5(7d  4)  35d  20
Example 3
Example 4
4(t  2)
10(2c  4)
Okay, so remember, the -4 is multiplying
the t AND the +2.
Okay, so remember, the -10 is multiplying
the 2c AND the -4.
Arrows and boxes…
Arrows and boxes…
4 (t  2)
And so we get…
4  t   4t
4  2   8
10 (2c  4)
a negative
x a positive
So long as you are good with negative
numbers, you should have been able to get
those signs correct!
4(t  2)   4t  8
Be careful with your signs…
10  2c   20c
10   4  40
a negative x
a negative
The 2nd multiplication always catches
people out. Remember, two negatives
multiplied together give a POSITIVE!
10(2c  4)   20c  40
Time for the stinkers…
Example 5
Example 6
5a(2b  c)
7ar (10st  2b  5)
Okay, so remember, the 5a is multiplying
the 2b AND the -c.
Okay, so remember, the 7ar is multiplying the
10st AND the +2b AND the -5.
Arrows and boxes…
Arrows and boxes…
5a (2b  c)
7ar (10st + 2b  5)
You need Rules of Algebra and Negative
Numbers for this…
7ar  10st  70arst
7ar  2b  14abr
5a  2b  10ab
5a   c   5ac
If you didn’t follow any of that, make sure
you go back and read over the 1. Rules of
Algebra notes again!
5a(2b  c)  10ab  5ac
Be careful with your signs and letters…
7ar   5   35ar
Again, if you missed any of that, you know
what to do…
7ar (10st  2b  5)  70arst  14abr  35ar
Too easy for you?…
Example 7
Example 8
4r (2r  9t )
2ab(4a  3ab2 )
Okay, so remember, the 4r is multiplying
the 2r AND the -9t.
Okay, so remember, the 2ab is multiplying the
4a AND the -3ab2
Arrows and boxes…
Arrows and boxes…
4r (2r  9t )
2ab (4a  3ab2 )
You definitely need your Rules of Algebra for
this…
4r  2r  8rr  8r
2ab  4a  8aab  8a 2b
2
4r   9t   36rt
2ab   3ab 2   6aabbb   6a 2b3
The first one was the tricky bit there!
Something, multiplied by itself, becomes
squared!
4r (2r  9t )  8r 2  36rt
How well do you know your algebra?…
That’s about as difficult as they get!
2ab(4a  3ab2 )  8a 2b  6a 2b3
And I think that’ll do!
Good luck with
your revision!