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,   x2

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) = x2
So the answer is 35x2

Let's look at another...

(8x3)(2x5)
First: (8)(2) = 16
Then: (x3)(x5) = (x3+5) = x8
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:

(3xy3)(6xz)
The rules stay the same.
First: (3)(6) = 18
Next: (xy3)(xz) = x2y3z
So the answer is: 18x2y3z

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:

(-4x2)(7y5z3)
First: (-4)(7) = -28
Then: (x2)(y5z3) = x2y5z3
So the answer is: -28x2y5z3


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