Who ever heard the word algebra? This is a branch of mathematics in problem solving using letters to represent numbers. Derived from Arabic, al-jabr which means completion. Do you know who the inventor is? He is a scholar named Al-Khawarizmi. Now, let’s look more closely at definitions and forms of algebra in more depth!
Algebraic uses are used for many fields of study such as mathematics, chemistry, biology, economics, and so on. Well usually, before being resolved, problems are written first in the form of algebra. How is that?
A. Form of Algebra
Consists of constants (fixed values) and variables (changing values) through addition, subtraction, multiplication, division, rebar and rooting operations. Example:
You can understand the examples above if you know the definitions of terms, factors, coefficients, constants, similar and non-similar tribal variables.
1. Tribe is a part of an algebraic form separated by a sign – or +
9a + 2b consists of two terms namely 9a and 2b.
3n2 – 2n – n consists of three terms, namely 3n2, 2n, and n.
The mention of two tribes is called binom, three tribes are called trinom, while many tribes are named polynomials. However, if only a tribe is usually called a single tribe.
2. Factors are numbers that divide up other numbers or times
For example: m x n x o or m.n.o or mno. Then, the factors are m, n, and o.
3. The coefficient is a number factor in a product with a variable.
If there is a coefficient whose value is equal to 1, then you don’t need to write it. If 1a – 1b – 1c simply write a – b – c.
Example: 5×3 + 2y – 2 then 5 is the coefficient of x3, while 2 is the coefficient of y.
4. Constants are symbols that state a certain number (constant / fixed number).
Example: 9a2 + 8b – 3 then term 3 is a constant
5. Similar and non-similar tribes
It is said to be similar if it contains variables and ranks of the same variable. If both are different, it is called a non-similar tribe.
Example: 2pq + 5pq then called a similar tribe, while 2xy + 3n is called a non-similar tribe.
B. Calculating operations
You notice the component below!
5 + 5 + 5 abbreviated to 3 x 5 or 3 (5)
n + n is abbreviated to 2 x n or 2n
4 x 3 x a x b is abbreviated as 12ab
Understood? Now we try to enter the number in the count operation.
1. Addition and repetition of algebraic forms
Simplify the form of 5a – 2b + 6a + 4b – 3c
5a – 2b + 6a + 4b – 3c = 5a + 6a – 2b + 4b – 3c
= (5 + 6) a + (-2 + 4) b – 3c
= 11a + 2b – 3c
Subtract 9a – 3 from 13a + 7
(13a + 7) – (9a – 3) = 13a + 7 – 9a + 3
= 13a – 9a + 7 + 3
= 4a + 10
2. Addition and subtraction of algebraic forms according to lanes or similar tribal columns
3. Declare multiplication of constants with two terms as the sum or difference
Distributive multiplication of addition and subtraction
Addition: a x (b + c) = ab + ac
Reduction: a x (b – c) = ab – ac
By using distributive multiplication, then the multiplication of constants with two terms can be expressed as the amount or difference. Example: