Can someone tell me the 6 class summary of algebra!?✨
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Answer:
see,dear actually Math chapters never have their summaries but basically I can explain u that algebra consists of variable, constant N arithmetic operators....
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Answer:
ok OKAlgebra is a branch of mathematics that can substitute letters for numbers to find the unknown. It can also be defined as putting real-life variables into equations and then solving them. The word Algebra is derived from Arabic “al-jabr”, which means the reunion of broken parts. Below are some algebra problems for students to practice.
Introduction to Algebra
Variable
A variable is an unknown quantity that is prone to change with the context of a situation.
Example: In the expression 2x+5, x is the variable.
Constant
Constant is a quantity which has a fixed value. In the given example 2x+5, 5 is the constant.
Terms of an Expression
Parts of an expression which are formed separately first and then added or subtracted, are known as terms.
In the above-given example, terms 2x and 5 are added to form the expression (2x+5).
Factors of a term
Parts of an expression which are formed separately first and then added or subtracted, are known as terms.
Factors of a term are quantities which cannot be further factorised.
In the above-given example, factors of the term 2x are 2 and x.
Coefficient of a term
The numerical factor of a term is called the coefficient of the term.
In the above-given example, 2 is the coefficient of the term 2x.
Like and Unlike Terms
Like terms
Terms having the same variables are called like terms.>
Example: 8xy and 3xy are like terms.
Unlike terms
Terms having different variables are called, unlike terms.
Example: 7xy and -3x are unlike terms.
Monomial, Binomial, Trinomial and Polynomial Terms
Name Monomial Binomial Trinomial Polynomial
No. of terms 1 2 3 >3
Example 7xy (4x−3) (3x+5y−6) (6x+5yx−3y+4)
Formation of Algebraic Expressions
Combinations of variables, constants and operators constitute an algebraic expression.
Example: 2x+3, 3y+4xy, etc.
Addition and Subtraction of Algebraic Expressions
Addition and Subtraction of like terms
Sum of two or more like terms is a like term.
Its numerical coefficient will be equal to the sum of the numerical coefficients of all the like terms.
Example: 8y+7y=?
8y
+7y
___________
(8+7)y = 15y
____________
Difference between two like terms is a like term.
Its numerical coefficient will be equal to the difference between the numerical coefficients of the two like terms.
Example: 11z−8z=?
11z
−8z
__________
(1-8)z = 3z
___________
Addition and Subtraction of unlike terms
For adding or subtracting two or more algebraic expressions, like terms of both the expressions are grouped together and unlike terms are retained as it is.
Addition of −5x2+12xy and 7x2+xy+7x is shown below:
−5x2+12xy
7x2+xy+7x
__________
2x2+13xy+7x
__________
Subtraction of −5x2+12xy and 7x2+xy+7x is shown below:
−5x2+12xy
−7x2+xy+7x
__________
12x2+11xy−7x
__________
Algebra as Patterns
Related Video:
Number patterns
If a natural number is denoted by n, then its successor is (n + 1).
Example: Successor of n=10 is n+1=11.
If a natural number is denoted by n, then 2n is an even number and (2n+1) is an odd number.
Example: If n=10, then 2n=20 is an even number and 2n+1=21 is an odd number.
Related Video:
Patterns in Geometry
Some geometrical figures follow patterns which can be represented by algebraic expressions.
Example: Number of diagonals we can draw from one vertex of a polygon of n sides is (n – 3) which is an algebraic expression.
Algebra-1
Geometric shapes and their diagonals
Algebraic expressions in perimeter and area formulae
Algebraic expressions can be used in formulating perimeter of figures.
Example: Let L be the length of one side then, the perimeter of :
An equilateral triangle = 3L.
A square = 4L.
A regular pentagon = 5L.
Algebraic expressions can be used in formulating area of figures.
Example: Area of :
Square = l2 where l is the side length of the square.
Rectangle = l * b, where l and b are lengths and breadth of the rectangle.
Triangle = 1/2 b * h where b and h are base and height of the triangle