ALGEBRA
Algebra is a branch of mathematics that uses symbols and mathematical operations, such as
addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
The word "algebra" comes from the Arabic الجبرal-jabr which means restoration or completeness,
and it comes from a treatise written in 830 by the medieval Persian mathematician Al-
Khwarizmi. Algebra is a branch of mathematics that studies structures, connections and
quantities. Algebra is usually used to solve a problem in various fields of study, such as
mathematics, chemistry, biology, economics, and so on.
A. Algebraic Forms
The algebraic form consists of constants, variables, and coefficients that are connected through
addition, subtraction, multiplication, division, power and root operations.
Coefficient Operator
5x + 3y + 9 = 28
Variable Constant
If you notice, the algebraic form above consists of the letters x and y as variables, numbers 5 and
3 as coefficients, and numbers 9 and 28 as constants. Constants are fixed values, so their values are self-
explanatory. Meanwhile, a variable is a value that is not fixed, so it can change. Then, variables can be
symbolized using letters, for example a, b, c, x, y, and so on. Finally, the coefficient is the value in front
of the variable. A variable must have a coefficient. Examples of other algebraic forms, among others, are
as follows:
,1. Term, which is a constant, or variable, or variable and its coefficients. Between terms can be
combined using addition or subtraction operations.
Example:
• 8, consisting of one term which is a constant.
• 9a + 2b, consisting of two terms, namely 9a and 2b which are connected using the addition
operation.
• 3n2 - 2n - n, consists of three terms, namely 3n2, 2n, and n which are connected using
subtraction operations.
Term can be divided into similar and dissimilar terms. It is said to be like terms if the variable
and the rank of the variable are the same. However, if the two are different, it is called a
dissimilar terms.
Example:
• 2p2q + 5p2q are called like terms because the variables and the power of the variables are the
same.
• 2xy2 + 2x2y is called an unequal term because the variable and the power of the variable are
not the same.
2. a factor is a number that is evenly divisible by another number.
For example: m × n × o or m⋅n⋅o, the factors are m, n, and o.
, B. Algebraic Calculation Operations
Okay, now that you know the forms and terms in algebra, now let's get into how to solve
algebraic form operations, shall we. We discuss three operations of algebraic forms first, namely
addition, subtraction, and multiplication.
1. Addition of algebraic forms
The condition for an algebra can be added is that the terms must be the same. Hey, do you still
remember the meaning of similar tribes? So, so that you understand better, let's try to do some of
the following examples, okay?
example:
Simplify the form from 5a - 2b + 6a + 4b - 3c.
The solution is easy, really. We only need to arrange or group similar terms. Similar terms mean
that the variables must be the same. After grouping, we can just add up the coefficients.
5a - 2b + 6a + 4b - 3c
= 5a + 6a - 2b + 4b - 3c
= (5 + 6)a + (-2 + 4)b - 3c
= 11a + 2b - 3c
2. Subtraction of algebraic forms
Just like algebraic addition operations, we can only perform algebraic subtraction operations if
the terms are the same. Example:
Subtract 9a - 3 from 13a + 7.
(13a + 7) - (9a - 3)
= 13a + 7 - 9a + 3
= 13a - 9a + 7 + 3
= (13 - 9)a + 10
= 4a + 10
3. Addition and subtraction of algebraic forms according to rows or columns of like
terms
Algebra is a branch of mathematics that uses symbols and mathematical operations, such as
addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
The word "algebra" comes from the Arabic الجبرal-jabr which means restoration or completeness,
and it comes from a treatise written in 830 by the medieval Persian mathematician Al-
Khwarizmi. Algebra is a branch of mathematics that studies structures, connections and
quantities. Algebra is usually used to solve a problem in various fields of study, such as
mathematics, chemistry, biology, economics, and so on.
A. Algebraic Forms
The algebraic form consists of constants, variables, and coefficients that are connected through
addition, subtraction, multiplication, division, power and root operations.
Coefficient Operator
5x + 3y + 9 = 28
Variable Constant
If you notice, the algebraic form above consists of the letters x and y as variables, numbers 5 and
3 as coefficients, and numbers 9 and 28 as constants. Constants are fixed values, so their values are self-
explanatory. Meanwhile, a variable is a value that is not fixed, so it can change. Then, variables can be
symbolized using letters, for example a, b, c, x, y, and so on. Finally, the coefficient is the value in front
of the variable. A variable must have a coefficient. Examples of other algebraic forms, among others, are
as follows:
,1. Term, which is a constant, or variable, or variable and its coefficients. Between terms can be
combined using addition or subtraction operations.
Example:
• 8, consisting of one term which is a constant.
• 9a + 2b, consisting of two terms, namely 9a and 2b which are connected using the addition
operation.
• 3n2 - 2n - n, consists of three terms, namely 3n2, 2n, and n which are connected using
subtraction operations.
Term can be divided into similar and dissimilar terms. It is said to be like terms if the variable
and the rank of the variable are the same. However, if the two are different, it is called a
dissimilar terms.
Example:
• 2p2q + 5p2q are called like terms because the variables and the power of the variables are the
same.
• 2xy2 + 2x2y is called an unequal term because the variable and the power of the variable are
not the same.
2. a factor is a number that is evenly divisible by another number.
For example: m × n × o or m⋅n⋅o, the factors are m, n, and o.
, B. Algebraic Calculation Operations
Okay, now that you know the forms and terms in algebra, now let's get into how to solve
algebraic form operations, shall we. We discuss three operations of algebraic forms first, namely
addition, subtraction, and multiplication.
1. Addition of algebraic forms
The condition for an algebra can be added is that the terms must be the same. Hey, do you still
remember the meaning of similar tribes? So, so that you understand better, let's try to do some of
the following examples, okay?
example:
Simplify the form from 5a - 2b + 6a + 4b - 3c.
The solution is easy, really. We only need to arrange or group similar terms. Similar terms mean
that the variables must be the same. After grouping, we can just add up the coefficients.
5a - 2b + 6a + 4b - 3c
= 5a + 6a - 2b + 4b - 3c
= (5 + 6)a + (-2 + 4)b - 3c
= 11a + 2b - 3c
2. Subtraction of algebraic forms
Just like algebraic addition operations, we can only perform algebraic subtraction operations if
the terms are the same. Example:
Subtract 9a - 3 from 13a + 7.
(13a + 7) - (9a - 3)
= 13a + 7 - 9a + 3
= 13a - 9a + 7 + 3
= (13 - 9)a + 10
= 4a + 10
3. Addition and subtraction of algebraic forms according to rows or columns of like
terms
