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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