Algebra and Its Application part 1 (Basic)

Nanda Putri Amalia
11313244012
International Mathematics Education 2011

From Marsigit's book (MATHEMATICS for Junior High School)
Chapter 1
Algebra and Its Application

Do you still remember the meaning of algebraic expression? Let see the following illustration.
Suppose Nanda is going to buy 5 books and 4pencils. If one book and one pencil are priced x rupiah and y rupiah, how much money that have to bring by Nanda?
Nanda have to bring 5x - 4y rupiahs.
The form of 5x + 4y from the above illustration is an algebraic expression in which:
5x and 4y are called terms,
x and y are variables
5 is the coefficient of 5x
4 is the coefficient of 4y
We can conclude that Algebraic expression is a statement consisting meaningful of coefficients and variables.

The Operations of Algebraic Expression.

Addition and Subtraction
In algebraic expression, we can only add and subtract the similar terms or like terms. The like terms contain the same variable with the same exponent.
There are two steps to add or subtract the algebraic expression.
1. group the like terms.
2. operate each group by adding or subtracting.

Multiplication Operation
1. Multiplication of one term and two terms of algebraic expressions.
this operations follow the distributive characteristic.
a(x+y)=ax+ay or (x+y)a=ax+ay
a(x -y)=ax-ay or (x-y)a=ax-ay
2. Multiplications of two terms and two terms algebraic expressions.
these multiplication can also be done using the distributive characteristics or using multiplication scheme.
(x+y)(a+b)= x(a+b)+y(a+b) = xa+xb+ya+yb

Exponential Operation
1. Understanding the Exponential
Exponential is a recur multiplication of a number. You can expand p^n as follow.
p^n= p.p.p.p.p} n term
example:
2^2 = 2.2 = 4
(3^2)^3 = 3^2 . 3^2 . 3^2 = 3.3 . 3.3 . 3.3 = 3^6

Divisions
1. Divisions of Algebraic expresions containing one terms
In the division of algebraic expressions is known two key terms:

• divisions with similar terms, such as 4x : x



• divisions with different terms, such as x^2 : x

Example

(x^3+3x) : x = (x^3 : x) + (3x : x)

= x^2 + 3