Expression
Numbers, symbols, and operators (such as + and ×) grouped together to show the value of something.
Examples:
• 2 + 3 is an expression
• 3 − x/2 is also an expression
Note: an expression does not have an equals sign. In fact none of these: = ≠ < > ≤ ≥
What is an Equation?
An equation says that two things are equal. It will have an equals sign “=” like this:
x | + | 2 | = | 6 |
That equation says: what is on the left (x + 2) is equal to what is on the right (6)
So an equation is like a statement “this equals that“
Here we have an equation that says 4x − 7 equals 5, and all its parts:
A Variable is a symbol for a number we don’t know yet. It is usually a letter like x or y.
A number on its own is called a Constant.
A Coefficient is a number used to multiply a variable (4x means 4 times x, so 4 is a coefficient)
Variables on their own (without a number next to them) actually have a coefficient of 1 (x is really 1x)
Sometimes a coefficient is a letter like a or b instead of a number:
Example: ax2 + bx + c
- x is a variable
- a and b are coefficients
- c is a constant
An Operator is a symbol (such as +, ×, etc) that shows an operation (ie we want to do something with the values).
A Term is either a single number or a variable, or numbers and variables multiplied together.
An Expression is a group of terms (the terms are separated by + or − signs)
Exponents
The exponent (such as the 2 in x2) says how many times to use the value in a multiplication.
Examples:
82 = 8 × 8 = 64
y3 = y × y × y
y2z = y × y × z
Polynomial
Example of a Polynomial: 3x2 + x – 2
A polynomial can have constants, variables, and the exponents 0,1,2,3,…
But it never has a division by a variable.
Monomial, Binomial, Trinomial
There are special names for polynomials with 1, 2 or 3 terms:
Like Terms
Like Terms are terms whose variables (and their exponents such as the 2 in x2) are the same.
In other words, terms that are “like” each other. (Note: the coefficients can be different)
Example:
(1/3)xy2 | −2xy2 | 6xy2 |
Are all like terms because the variables are all xy2