E-STAR - Student

Mathematical expressions can be numerical or algebraic.
If a mathematical expression involves only numbers and operations, then it is called a numerical expression. Example: 8 ÷ 2 + 2 × 10 – 3
If a mathematical expression involves numbers, variables and operations, then it is called an algebraic expression. Example: 2x² + 3xy – 2
The letter or symbol in an algebraic expression is called a variable.
The number that the variable is being multiplied by is called the coefficient
Any number not joined to a variable is called a constant.
The parts of an algebraic expression that are separated by addition or subtraction signs are called terms.
Two or more terms that have EXACTLY the same variables are called like terms.
Like terms can be added or subtracted by adding or subtracting their coefficients
Algebraic expressions can be evaluated by substituting the values of the variables
An algebraic expression of the form a(x + y) can be expanded or distributed as ax + ay using the distributive laws.
Factorization of an algebraic expression is just the reverse operation of expanding an expression. ax + ay is factorized by taking the common factor of the two terms as a(x + y). Factorization is the reverse process of expansion of an algebraic expression.

An algebraic expression having only one term is called a monomial.
An algebraic expression having only two terms is called a binomial.
An algebraic expression having tree terms is called a trinomial.
Any two binomials can be multiplied as:
(x + y)(a – b) = x(a – b) + y(a – b)
The square of a binomial is a product obtained by multiplying the binomial with itself.
For example, (x + y) (x + y) = (x + y)² = x² + 2xy + y²
(x – y) (x – y) = (x – y)² = x² – 2xy + y²
The square of a binomial gives a trinomial which is a perfect square
The difference of two perfect squares like m² – n² is called difference of two squares and is expanded as m² – n² = (m – n) (m + n)
Quadratic expressions of the form ax² + bx + c can be factorized and written as a product of two linear factors. To factorize quadratic expressions we usually find two numbers whose sum is the coefficient of the middle term b and product a × c = ac.