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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
x(y + 3) can be multiplied out to give xy + 3x which means exactly the same as x(y
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
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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The next technique tells us how to find out what x is.
4. Gather like terms
When you gather like terms, all you do is find things which are the same and try to
lump them together.
2x + 4 = 3x
Here 3x and 2x are both applied to x, so we can use yet another technique,
subtracting from both sides of the equation.…read more