# Multiplying Brackets and Pascal's Triangle 1 Row 0 1

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```							                                                                                      d” sb

Multiplying Brackets and Pascal’s Triangle
We can multiply more complicated brackets

It works like this

e.g. (x + 5)(x2 + 2x + 4)                   x (x2 + 2x + 4) + 5(x2 + 2x + 4)
x3 + 2x2 + 4x + 5x2 + 10x + 20
x3 + 7x2 + 14x + 20

1) (x + 3)(x2 + 4x + 2)                           2) (x + 5)(x2 + 5x + 6)

3) (x + 3)(x2 + x + 1)                            4) (x + 1)(x2 - 3x + 2)

5) (x + 4)(x2 - 2x - 2)                           6) (x - 10)(x2 + 2x + 3)

7) (x - 3)(x2 + 5x - 4)                           8) (x - 2)(x2 - 3x - 7)

9) (x - 3)(x2 - x + 2)                           10) (x + 10)(x2 + 10x - 1)

11) (x2 + 4x + 2) (x2 + 3x + 5)                  12) (x2 - 5x + 1) (x2 - 2x - 3)

Pascal was a famous French mathematician who lived about 350 years ago

This is his triangle:

1                           Row 0
1          1                     Row 1
1         2              1            Row 2
1         3           3           1        Row 3
1         4         6             4       1    Row 4

IN YOUR BOOK Copy out Pascal’s triangle

Add rows 5, 6, 7 8

If you are not sure how to do it, there is a clue below

The ‘parents’ of 4 are 1 and 3. The ‘parents’ of 6 are 3 and 3
d” sb

Now look at this

(x + 4)3 = (x + 4) (x + 4) (x + 4)

We can easily work out (x + 4) (x + 4)      x2 +8x +16

So (x + 4)3 = (x + 4) (x2 +8x +16)

= x (x2 +8x +16) + 4 (x2 +8x +16)

= x3 + 8x2 + 16x + 4x2 + 32x + 64

= x3 + 12x2 + 48x + 64

IN YOUR BOOK Work out these

1) (x + 1)3

2) (x + 1)4

3) (x + 1)5

Can you see the connection that this has with Pascal’s triangle?

Can you write down the answers to these straight away?

4) (x + 1)6

5) (x + 1)7

6) (x + 1)8

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