# Learning Aid #1: Algebraic Expressions

As we continue the study of Algebra, we will see that Algebra has a language of its own.this language consists of various mathematical symbols, numerical phrases and sentences, coefficients, exponents and powers.This expressions in Algebra allows us to show the relations between quantities thereby arriving to solutions of certain problems.
An important goal of Algebra is learning its use as a problem-solving tool.many of the problems in this course would require us to make use of formulas, from which the world owes so much for what it is today.

Concepts and Terminologies

1. Algebraic Expression - any combination of symbols and numbers related by the plus (+) or minus (-) signs.
Examples: 7x2-2x+3, 4y+5, 5y+9y-3x+8
2. Equivalent Expressions - two algebraic expressions having the same value for the same replacement of the variabe.
Examples: x+4 and 2x+8, x2-5 and x(x-5)
3. Evaluating an Algebraic Expression - the process of replacing the value of the variable by a given value then performing the indicated operations to obtain a single numerical value for the given algebraic expression.
4. Polynomial - an algebraic expression involving only addition and multiplication of numbers and variables.if the term in the algebraic expression has a variable in the denominator, then the algebraic expression is not a polynomial.
Examples: 4x2 , x3-1/3 are polynomials, 8/x2-2/7 is not a polynomial
5. Term - is a part of an algebraic expression included between two consecutive + or - sign.
Examples: 2a + 3b the terms are 2a and 3b

Concepts of Polynomials
:Classification of Polynomials

1. Monomial - a polynomial with only one term.
Examples: x, 5m, -6x2,7 are all monomials
2. Binomial - a polynomial with two terms.
Examples: 2x+4y, 6a3+3b, 3m2-5n3
3. Trinomial - a polynomial with three terms.
Examples: 5x3-3x2+x, a+b+c
4. Multinomial - a polynomial with 4 or more terms.
Examples: 3m4-5m3-4m2+2m+8, a-b+c-d