ALGEBRAIC EXPRESSIONS
An algebraic expression is any representation of a number by algebraic notation.
Degree 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 = 4×2 + 4xt + t2
Here we have six terms
Similar (like) terms are terms having the same variables affected by the same exponents
EXAMPLE
5×2 and 2×2 are similar terms
2ab and 4ab
y and 2y
Dissimilar (unlike) terms are terms which differ in variables or exponents, or both.
Program 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 Online
2a2b3 the degree is 5
4xy the degree is 2
2abc3 the degree is 5
Homogeneous terms are terms with the same degree
EXAMPLE oneline
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 online
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 2×2 + 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
