Question

Identify the greatest common factor (GCF). If needed, when typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. 30x^2y-45x^2y^2+135xy^3The GCF is Answer

Answer 1

Step-by-step explanation:

The greatest common factor is the factor that is common to all the terms in the given expression.

Given the expression:

`30x^2y-45x^2y^2+135xy^3`

Find the factors of each term

`\begin{gathered} 30x^2y=15*2* x* x* y \\ 45x^2y^2=15*3* x* x* y* y \\ 135xy^3=15*9* x* y* y* y \end{gathered}`

From the following factors, we can see that the common factors are 15, x, and y.

Taking their products to get the Greatest Common Factor

`\begin{gathered} \text{GCF}=15* x* y \\ \text{GCF}=15xy \end{gathered}`

Hence the GCF of the expression is 15xy