## Basics

### Now, what is algebra?

*Erm… Don’t you have a math textbook???*

Never mind…

In primary schools, we often use the “trial and error” method to solve questions involving algebraic expressions. Now, in our secondary years, we are expected to use more advanced techniques to solve these problems rather than guessing and solving.

Here is a simple example:

By dividing the whole equation by 2, we get

Lastly subtracting 7 from the whole equation gives us

From this basic problem involving a variable , we can see that algebra is a branch of mathematics that uses letters to represent unknowns, and in fact, it can also be used as a tool to aid one in solving problems which include several unknowns. Algebra also studies the different concepts, theorem and formulas arising from these algebra problems to solve equations or inequations. One of the many theorems is the Binomial Theorem, which we will cover in a later time.

**Here are some basic terms about algebra…**

Constant: A value that is non-varying and remain unchanged

Parameter: Basically it’s another term for ‘constant’

Variable: A value that may change and vary according to the given expression

Coefficient: The numerical multiplicative factor of an algebraic expression

Monomial: The product of variables and numerical factors(constants)

**Note: The power of variables must be a positive integer, eg and are not monomials.*

Polynomial: The sum of monomials

**Interesting facts: Sum/Difference/Product of polynomials = Polynomials; Division of polynomials need not to be a polynomial.*

Eg. The expression

- Is a polynomial
- Constant/Parameter =
- Variable =
- Coefficient = 4 for ; -5 for ; 3 for
- Monomials = , , and

**Basic algebra manipulation**

Multiplying 2 negative values gives one a positive value

If a negative sign is in front of a bracket, all the + and – signs in the bracket will reverse it signs.

*Eg.**But why is this so? *Hint: Treat the negative sign as ‘-1'**(See Distributive Law)*

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