Question

How do you multiply monomials by monomials?

Answer 1

`=> 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`

Answer 2

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`.