How do you multiply monomials by monomials?

2 Answers
NJ
Mar 27, 2018

#=> a_1x^(p_1) * a_2x^(p_2)=a_1a_2x^(p_1+p_2)#

Explanation:

A monomial is of the form:

#=> ax^p#

where #a# is a constant coefficient and #p# is a constant power.

In the case of multiplying two monomials together:

#=>Ax^P equiv a_1x^(p_1) * a_2x^(p_2)#

The coefficients will multiply, so:

#=> A =a_1 * a_2#

The powers will sum, so:

#=> P =p_1 + p_2#

Hence:

#=> Ax^P equiv a_1x^(p_1) * a_2x^(p_2)=a_1a_2x^(p_1+p_2)#

For example:
#=>3x^2*2x#

#=> (3*2)x^(2+1)#

#=> 6x^3#

The Legend
Mar 27, 2018

Multiply all the numbers and variables together (use the Product of Powers Rule for exponents) and simplify.

Explanation:

Here's an example:
#2x^2y^4z*4a^3x^3z^3#
We see that we have two numbers, two #x#'s, one #a#, one #y#, and two #z#'s. We can use the Product of Powers Rule to simply add the exponents for the #x#'s and #z#'s. #2*4=8, x^2*x^3=x^5, and z*z^3=z^4#. So #2x^2y^4z*4a^3x^3z^3=8a^3x^5y^4z^4#.

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