CBSE Class 7 Maths Notes Chapter 12 Algebraic Expressions

Algebra plays a crucial role in understanding and describing patterns in mathematics. It provides a systematic way to identify, analyze, and represent patterns using symbols, variables, and equations. By recognizing patterns, mathematicians and scientists can make predictions, formulate theories, and solve complex problems in various fields. In algebra, patterns can manifest in different forms, such as numerical sequences, geometric shapes, or functional relationships. Algebraic expressions and equations are used to describe these patterns and establish relationships between variables and constants. For example, in a sequence of numbers, algebra can be used to find the rule or pattern governing the sequence, allowing us to predict the next term or term at any position. Similarly, in geometry, algebraic expressions can represent the relationships between the dimensions of geometric figures, allowing us to calculate areas, perimeters, volumes, and other properties.

Writing Number patterns and rules related to them

• If a natural number is denoted by n, its successor is (n + 1). Example: Successor of n=10 is n+1 =11.
• If a natural number is denoted by n, 2n is an even number and (2n+1) an odd number. Example: If n=10, then 2n = 20 is an even number and 2n+1 = 21 is an odd number.

Writing Patterns in Geometry

Geometry involves the study of shapes, sizes, and properties of objects in space. Algebraic expressions are often used to describe patterns and relationships in geometric figures.

Example: Number of diagonals we can draw from one vertex of a polygon of n sides is (n – 3).

Definition of Variables

In algebra, expressions can contain variables and constants. Here's a breakdown:

Variable:

• A variable is a quantity that can vary or change within a given context.
• Variables are typically represented by letters from the alphabet, such as a, a,x,p etc.
• These letters denote quantities whose values are not fixed and may change depending on the situation.
• For example, in the equation y= mx+b, both x and y are variables representing quantities that can vary.

Constant:

• A constant is a quantity that has a fixed value and does not change.
• In algebraic expressions, constants are numerical values that remain the same throughout.
• For instance, in the expression $4$ , the constant is $4$ since its value does not depend on any variable.
• The terms 5 $x$ and 4 in the expression are also called terms of the expression.
• In the term $5x$ , $5$ is termed the coefficient of $x$ , representing the numerical factor of the variable.
• Coefficients are essential in understanding how variables interact within an expression.

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Monomial, Binomial, Trinomial and Polynomial Terms

Monomial:

• A monomial is an algebraic expression that consists of only one term.
• It can be a constant, a variable, or a product of constants and variables.
• Examples of monomials include  7xy, −5m, etc.

Binomial:

• A binomial is an algebraic expression that consists of two terms connected by addition or subtraction.
• Each term in a binomial can be a monomial.
• Examples of binomials include  5mn+4, x+y, etc.

Trinomial:

• A trinomial is an algebraic expression that consists of three terms connected by addition or subtraction.
• Each term in a trinomial can be a monomial.
• Examples of trinomials include x+y+5, a+b+ab, etc.

Polynomial:

• A polynomial is an algebraic expression that consists of one or more terms connected by addition or subtraction.
• It can have any number of terms, making it a more general term that includes monomials, binomials, and trinomials.
• Examples of polynomials include x+y, 3xy+6+y, etc.