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Factoring multivariable polynomials involves finding the common factors among the terms of the polynomial and expressing it as the product of simpler polynomials.

Step-by-Step Process

To factor a multivariable polynomial, follow these steps:

1. Identify common factors among the terms of the polynomial.
2. Factor out the greatest common factor (GCF) from each term.
3. Express the polynomial as the product of the GCF and the remaining factors.
4. If possible, further factor the remaining polynomial using other factoring techniques such as grouping, difference of squares, or trinomial factoring.

Example

Let's factor the multivariable polynomial $$2x^{2}y+4x{y}^2$$:

Step 1: Identify common factors - The common factor among the terms is $$2xy$$.

Step 2: Factor out the GCF - $$2xy\left(x+2y\right)$$.

Step 3: The polynomial is now factored as $$2xy\left(x+2y\right)$$.

Factoring multivariable polynomials is essential in algebra and other areas of mathematics for simplifying expressions and solving equations.