algebraic expressions

http://www.freemathgenius.com. this video teaches about the fundamental terms in algebra. the explanations are vivid and you are can understand all the terms.

An algebraic expression is any representation of a number by algebraic notation.

EXAMPLE

3x, 4ab, 4y, 5a2

In an equation or inequality a term is an expression separated by a plus or minus sign or an equality or inequality sign.


EXAMPLE

3x -- 2a = 4c + 3

There are four terms, 3x, -2a, 4c, 3.

Note that when parenthesis is used it must be expanded to get the individual terms or it can be considered as one term despite being separated by a plus or minus sign


EXAMPLE

3(x+2) + 4y = (2x + t) 2

There are three terms, 3(x+2), 4y and (2x + t)2

You could have also expanded to remove the parenthesis

3x + 6 + 4y = 4x2 + 4xt + t2

Here we have six terms



Similar (like) terms are terms having the same variables affected by the same exponents

EXAMPLE

5x2 and 2x2 are similar terms 2ab and 4ab y and 2y

Dissimilar (unlike) terms are terms which differ in variables or exponents, or both.

EXAMPLE

4a and 5b are unlike because they have different variables 3t2 and 2t3 are dissimilar because they have different exponents 4ab and 4ac are different because they have different variables



The degree of a term is the sum of its exponents.

EXAMPLE

2a2b3 the degree is 5 4xy the degree is 2 2abc3 the degree is 5


Homogeneous terms are terms with the same degree

EXAMPLE

The degree for both 3ab and 2a2 is 2

The degree for both 2a2b3 and 2abc3 is 5



A monomial is an algebraic expression of one term.

EXAMPLE 2x

A polynomial is an algebraic expression of more than one term.

EXAMPLE

3y -2 or b + c or 3a -- 4b + 4

A polynomial of two terms is called a binomial

EXAMPLE
X2 + 3 or 3x -3 or a + b

A polynomial of three terms is called a trinomial.

EXAMPLE

2x + 3b = c or 2x2 + 3x -- 2 or a + b + c


The degree of an algebraic expression is the same as the degree of its highest term.

EXAMPLE

h2 + 2h -20 ---- the degree of the expression is 2 because of the term h2

4acd + 2ab + 3abcd ----- the degree of the expression is 4 because of 3abcd

Homogeneous polynomial is a polynomial with all its terms having the same degree

EXAMPLE

y2 -- 3xy + x2 -------------- the degree is 2

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