Definitions of Coefficient, Term, Constant Term, and Like Terms
In the previous lesson, you learned to distinguish between a __constant__ and a __variable__. These are the two components of what is called a __term__. Before looking at the exact definition, consider the following:
$$\displaystyle 2x+4y$$.
How many terms do you see?
Not quite!
What you counted was the number of constants and variables, not the number of terms.
Right!
A __term__ is the product of constant(s) and variable(s). The constant part of the term is called the __coefficient of the term__. Each term in an expression will be separated by a + or - symbol.
Therefore, $$2x+4y$$ has two terms.
Now try this example:
How many terms does $$3ab+c+7$$ have?
That's it!
A term can consist of _just_ a variable such as _c_. Also, a term can have no variable attached, in which case it would be called a __constant term__. The term 7 was an example of such a term.
Thus, 3_ab_, _c_, and 7 are all terms.
Incorrect.
A term can consist of _just_ a variable such as _c_. Also, a term can have no variable attached, in which case it would be called a __constant term__. The term 7 was an example of such a term.
Thus, 3_ab_, _c_, and 7 are all terms.
Now using the same example, $$3ab+c+7$$, from the definition you know that the coefficient of the term $$3ab$$ is 3.
What are the coefficients of the terms _c_ and 7?
Excellent!
Incorrect.
Incorrect.
The constant that is multiplying the variable _c_ is actually 1. So the coefficient of the term _c_ is 1. Also, since 7 is already a constant, it is the coefficient of the term.
Once you are able to identify and count terms, you are ready to recognize what are called __like terms__. These are terms with the _exact same variable parts_. In other words, like terms contain the exact same variables raised to the same powers.
This will be very important to understand since you can add and subtract terms only if they are like terms. So which of the following terms can you add?
(a) $$3xy^2$$
(b) $$3xy$$
(c) $$5xy^2$$
Be careful! Like terms must contain the exact same variables raised to the same powers, _not necessarily_ the same coefficients!
Therefore, the only two terms that are like terms and can be added together are $$3xy^2$$ and $$5xy^2$$.
Great!
The only two terms that are like terms and can be added together are $$3xy^2$$ and $$5xy^2$$.
To sum up:
[[summary]]
Incorrect.
A term can consist of _just_ a variable such as _c_. Also, a term can have no variable attached, in which case it would be called a __constant term__. The term 7 was an example of such a term.
Thus, 3_ab_, _c_, and 7 are all terms.
Four
Two
One
Two
Three
The coefficient of the term _c_ is 1, and the coefficient of the term 7 is 0.
The coefficient of the term _c_ is 0, and the coefficient of the term 7 is 7.
The coefficient of the term _c_ is 1, and the coefficient of the term 7 is 7.
(a) and (b)
(a) and (c)
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