1Cademy - Factoring $$8x^3y - 10x^2y^2 + 12xy^3$$

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Factoring the Greatest Common Factor from a Polynomial

Example

Factoring $8x^3y - 10x^2y^2 + 12xy^3$

Factor $8x^3y - 10x^2y^2 + 12xy^3$ by extracting the greatest common factor.

Step 1 — Find the GCF: The three terms are $8x^3y$ , $-10x^2y^2$ , and $12xy^3$ . The numerical GCF of $8$ , $-10$ , and $12$ is $2$ . The shared variables are $x$ and $y$ . The lowest power of $x$ is $x^1$ (or $x$ ), and the lowest power of $y$ is $y^1$ (or $y$ ). Therefore, the GCF is $2xy$ .

Step 2 — Rewrite each term using the GCF: Express each term as the product of the GCF and the remaining factors: $2xy \cdot 4x^2 - 2xy \cdot 5xy + 2xy \cdot 6y^2$

Step 3 — Factor out the GCF: $2xy(4x^2 - 5xy + 6y^2)$

Step 4 — Check by multiplying: $2xy(4x^2 - 5xy + 6y^2) = 2xy \cdot 4x^2 - 2xy \cdot 5xy + 2xy \cdot 6y^2 = 8x^3y - 10x^2y^2 + 12xy^3$ ✓

The factored form is $2xy(4x^2 - 5xy + 6y^2)$ . This demonstrates how to factor polynomials with multiple variables by finding the GCF for each variable independently.

Updated 2026-04-29

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OpenStax Intermediate Algebra

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