Mr F

1
Mr Fs Maths Notes

• Algebra
• 5. Double Brackets

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5. Double Brackets
You knew it was coming Just when you have got
your head around how to expand single brackets,
your lovely maths teacher announces its time to
have a go at expanding double brackets. But the
good news is that its no more difficult than
single brackets, you dont need to learn any new
skills, and you get loads more marks for doing
it!

• Skills you need for success
• If you know about these things, you will be fine
• How to expand single brackets (see Algebra 2.
  Single Brackets)
• Rules of Algebra (see Algebra 1. Rules of
  Algebra)
• Rules of Negative Numbers (see Number 8.
  Negative Numbers)

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Its all about FOIL Now, like with most things
in maths, there are a lot of different ways of
expanding double brackets, and if you are happy
with your way, then just stick to it, but here is
how I do it. FOIL basically tells me the order
in which I need to multiply terms, because the
most common mistake people make when expanding
double brackets is to miss a few terms out!
2
Some people call this the crab claw method!
1
3
4
F irst
Multiply together the first terms in each bracket
remembering to include the signs in front of
them
1.
O uter
Multiply together the terms on the outside each
bracket remembering to include the signs in
front of them
2.
I nner
Multiply together the terms on the inside each
bracket remembering to include the signs in
front of them
3.
L ast
Multiply together the last terms in each bracket
remembering to include the signs in front of
them
4.
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Example 1
Example 2
Until you get really comfortable, there is
nothing wrong with drawing the crab claw on to
remind you what to multiply!
Time for the crab claw
Be really careful with the NEGATIVES
First
First
Outer
Outer
Inner
Inner
Last
Last
Now we write down our answers, in order,
remembering if there is no sign in front of our
term its just a disguised plus!
Now we write down our answers, in order, making
sure we get all the signs correct!
Notice that the middle terms simplify to give
Notice that the middle terms simplify to give
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Example 3
Example 4
Lets draw our smiley face
Time for another smiley face
Be so, so, so careful with the NEGATIVES
Again, we must watch those NEGATIVES
First
First
Outer
Outer
Inner
Inner
Last
Last
Writing down our answers, we get
Once again, the signs are the key to success!
Carefully simplify the middle terms
You have to know your Rules of Negative Numbers
inside out for this next bit
6
Lets take a moment to reflect Just before we
look at a few more difficult ones (which, by the
way, follow the exact same rules as these), I
just want to draw your attention to the answers
we got
Now, look at the numbers in the questions and the
numbers in the answers. Can you see a quick way
of getting from one to the other?... Dont worry
if you cant, but if you can then you are one
step ahead, because that is the key to success at
6. More Factorising, which is coming up
soon But for now, how about some tricky
expanding double bracket questions?...
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Example 5
Example 6
Lets draw our smiley face
Are you still feeling happy?
Again, we must watch those NEGATIVES, and we must
know our Rules of Algebra!
NEGATIVES and Rules of Algebra again
First
First
Outer
Outer
Inner
Inner
Last
Last
Writing down our answers, we get
As always, the signs are the key to success!
Carefully simplify the middle terms
Carefully simplify the middle terms
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Example 7
Example 8 because I am feeling nasty
Lets draw our crab claw
Are you still smiling now?
Okay, you would be really unlucky to ever get one
as hard as this, but theres no reason we cant
do it
Again, we must watch those NEGATIVES, and we must
know our Rules of Algebra!
First
First
Outer
Outer
Inner
Inner
Last
Last
As always, the signs are the key to success!
Phew! Writing down our answers, we get
Can we simplify the middle two (or indeed, any)
of the terms?... NO because there are NO LIKE
TERMS!
Can we simplify the middle two (or indeed, any)
of the terms?... NO because there are NO LIKE
TERMS!
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Last one, I promise How would you do this
one?...
If you said well, its dead easy, isnt it, the
answer is just
Then please never say that again because its
wrong!
Remember squaring something means multiplying it
by itself. So, this question could actually be
written as
Which means we can go back to our friend FOIL,
and everyone is happy! Incidentally, if you want
to check you can still do these, the final
simplified answer is
Can you see how we could have reached that answer
a quicker way?
TO BE CONTINUED on a maths website near you
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• Good luck with your revision!