Chapter: Algebraic Expressions and Identities
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An expression having one or more variables is called an algebraic expression. An algebraic expression may or may not contain mathematical operators like the symbols of addition, subtraction and multiplication. The quantities in an algebraic expression - variable, constant or combinations of both, joined by plus or minus signs, are called its terms.
The elements whose product forms a term of an algebraic expression are called the factors of that term. The numerical factor of a term containing a variable is called the coefficient of the term.
Algebraic expressions that contain only one term are called monomials.
Algebraic expressions that contain only two terms are called binomials.
Algebraic expressions that contain only three terms are called trinomials.
Algebraic expressions with all variables having whole number exponents or powers are called polynomials. The expressions in which the powers of variables are negative or rational numbers are not polynomials.
An equation is true for only certain values of the variables and need not be true for all values of the variables. If it is true for all values of the variables in it, then it is called an Identity. These identities are obtained on multiplying one binomial with another binomial and are known as Standard Identities.
The four standard identities that we are going to learn in this lesson are:
  • (a + b)2 = a2 + 2ab + b2
  • (a - b)2 = a2 - 2ab + b2
  • (a + b)(a – b) = a2 – b2
  • (x + a)(x + b) = x2 + (a + b)x + ab
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