Question

Factor completely. $$ x^{4} y^{2}+12 x^{3} y^{3} $$

   Factor completely.
$$
x^{4} y^{2}+12 x^{3} y^{3}
$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 3rd Edition

Chapter 7, Problem 95

Instant Answer

Solved by Expert Narayan Hari

02/17/2021

Step 1

In this case, the common factors are \(x^{3}y^{2}\). Show more…

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Factor completely. $$ x^{4} y^{2}+12 x^{3} y^{3} $$

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Key Concepts

Greatest Common Factor (GCF)

The GCF is the largest expression, including both numerical coefficients and variable parts, that can divide each term of an algebraic expression without a remainder. It is foundational in simplifying and factoring polynomials by identifying common factors shared by all terms.

Extracting Common Monomial Factors

This process involves factoring out the common monomial (the GCF) from each term in an expression. By doing so, the expression is rewritten as a product of the common factor and a simpler polynomial, which is a critical step in complete factorization and further simplifies solving or manipulating the expression.

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