Monomial
Definition:
A term can be a variable, a number (called a constant), or a variable
with a number attached (called a coefficient).
Single terms are called "monomials". 
Examples of Monomials:
x, y, a, 12,
7, 2x, 9z, 5m, x^{2} 
Monomial: A single term
In^{ }this lesson we will learn how to multiply monomials. 
To multiply monomials
1.
If there are coefficients on the terms then we
must first multiply coefficients by coefficients.
2.Then we multiply the variable of one term by the variable in the other
term.
For example:
(3x)(4y)
First : (3)(4) = 12
Then: (x)(y) = xy
So the answer is: 12xy 
If the variable in one term is the same as the variable
in the other term then we must follow the rule of exponents for
multiplication.
For example: (5x)(7x)
First: (5)(7) = 35
Then (x)(x) = x^{2}
So the answer is 35x^{2} 
Let's look at another...
(8x^{3})(2x^{5})
First: (8)(2) = 16
Then: (x^{3})(x^{5}) = (x^{3+5}) = x^{8}
So the answer is 16x 
It's possible for there to be more than one variable in a term.
Let's look at an example of that:
(3xy^{3})(6xz)
The rules stay the same.
First: (3)(6) = 18
Next: (xy^{3})(xz) = x^{2}y^{3}z
So the answer is: 18x^{2}y^{3}z 
Finally we need to remember that when multiplying terms we must
also pay attention to the signs on the terms.
When multiplying remember:
(+)(+) = +
(+)() = 
()(+) = 
()() = +
Let's look at an example of this:
(4x^{2})(7y^{5}z^{3})
First: (4)(7) = 28
Then: (x^{2})(y^{5}z^{3}) = x^{2}y^{5}z^{3}
So the answer is: 28x^{2}y^{5}z^{3} 
^{
}It's time to practice...
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