# Secrets of Algebra

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- Created on: 05-06-11 16:04

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Secrets of Algebra

There are a few techniques which you should become familiar with which can be used to

make algebra easy.

1. Multiplying the brackets

You will use this a lot so make sure you understand how it works from studying the

examples below:

x(y + 3) can be multiplied out to give xy + 3x which means exactly the same as x(y

+ 3)

p(4 q) can be multiplied out to give 4p pq

2x(3x + 7y 2z) can be multiplied out to give 6x2 + 14xy 4xz

If you don't believe this then try substituting numbers for the shorthand codes:

Let p = 2 and q = 1.

p(4 q) = 2 times (4 minus 1) = 2 times 3 = 6

4p pq = 4 times p minus p times q = 8 2 = 6

2. Multiplying two lots of brackets

Another technique which you will use a fair bit:

To multiply out something like (x + 3) (x + 4), you need to multiply each part within

the brackets as shown in the steps below (the parts in red are the parts being

multiplied in that step).

(x + 3) (x + 4) = x2

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

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

(x + 3) (x + 4) = 12

Then simply add each of these to get the answer : x2 + 7x + 12

Note that 4x + 3x = 7x

3. CrossMultiplication

This is the easy way to rearrange a formula such as

When we crossmultiply we end up with 2(x + 2) = 3x

Now, we end up with the equation:

2x + 4 = 3x

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