An expression shows the relationship between numbers and variables and dimensions.
For example in the expression 4a2 + 6b - 8, the 4 means that there are 4 sets of a2 whilst the 6 signifies 6 sets of b and the -8 means that 8 is subtracted from the first two terms.
The a and b are known as variables, whilst the -8 is known as a constant.
A variable is an unknown. Variables are assigned letters "x," "y," "z," etc
As an example, in the equation x + y = 7 the values of x and y can be lots of different things. If x = 3 then y=4, if x=1 then y=6 etc.
The algebraic expression may have one or more variables. The variables may be raised to different powers. (i.e r x r x r = r3, z x z x z x z = z4 )
A term is the number and the attached variable. In the expression 6x2 - 2y , the 6x2 and the -2y are terms. The 6x2 tells us that there are six lots of x2 ( i.e 6 times x2) The 6 and 2 are known as numerical coefficients.
Like terms are numbers with the same variables with the same powers. So, in the expression 7m2 + 3n - 3m2 - 3m the like terms are 7m2 and -3m2
Like terms can be added and subtracted, for example 7m2 + 3n - 3m2 - 3m is the same as 4m2 + 3n - 3m .
Coefficients are numbers in front of variables. If there is not a number in front of a variable, the understood coefficient is "1." If there is a negative in front of a variable with no number in front of it, the coefficient is a negative one.
So, in the expression 4a2, the 4 means 4 lots of a2
The numbers that go in frontof variables are called Coefficients. If no number is before a variable then the coefficient is "1" (positive). If a negative is in front of a variable, without a number before it, then the coefficient is negative.