Let's hear it for MULTIPLYING monomials:
Multiplying monomials is easy as long as you think in terms of what the exponents really mean.
For example:
x^3 means x times x times x or (x)(x)(x)
x^5 = (x)(x)(x)(x)(x) ....... x times itself five times
So if we want to multiply X^3 times x^5 we are really looking at this:
(x)(x)(x) times (x)(x)(x)(x)(x)
which equals
(x)(x)(x)(x)(x)(x)(x)(x)
or more commonly x^8
*basicly, you just add the exponents
Now let's try one with several different variables:
x^2y times z^3xy^6
This literally means:
(x)(x)(y) times (z)(z)(z)(x)(y)(y)(y)(y)(y)(y)
We can rearrange these using the
commutative property of multiplication. Then we can use the associative
property of multiplication to group all the x's, y's, and z's together
and multiply to achieve our final answer.
[(x)(x)(x)] [(y)(y)(y)(y)(y)(y)] [(z)(z)(z)]
Put more simply x^3y^7z^3
*once again you are really just adding
the exponents. Don't forget the understood exponent of one
on the "y" in x^2y
Now let's see what
happens when we incorporate numerical coefficients in the front of each
monomial.
Multiply 3xy^2 times -7x^2y.
This literally means:
3(x)(y)(y) times -7(x)(x)(y)
Rearrange and group as above, placing the coefficients in front.
[(3)(-7)] [(x)(x)(x)] [(y)(y)]
Or in simplified form, -21x^3y^2
*JUST A REMINDER: remember that the coefficient on the term -x is (-1). Even though you don't see it, it is "understood" to be there.
Now you try a few. Click the answer link to see if you are right.
- r(r^3)(-r^5) = ? answer
- (4uv)(u^2)(8v^4u^2) = ? answer
- (4b^2)(1/4abc^3)(-c) = ? answer
