Question

Factor. $$15 y^{2}-2 x y^{2}-x^{2} y^{2}$$

Name: Problem 71, Chapter 10: Prealgebra and Introductory Algebra
Uploaded: 2020-06-25T20:29:17-08:00
Duration: 1 min 52 s
Channel: Jason Taylor-Pestell
Description: Factor. 15 y^2-2 x y^2-x^2 y^2

   Factor.
$$15 y^{2}-2 x y^{2}-x^{2} y^{2}$$

Prealgebra and Introductory Algebra

Richard N. Aufmann,… 3rd Edition

Chapter 10, Problem 71

Instant Answer

Solved by Expert Jason Taylor-Pestell

06/25/2020

Step 1

We notice that all terms have a $y^{2}$ in common. So, we factor out $y^{2}$ from each term. $$y^{2}(15 - 2x - x^{2})$$ Show more…

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Factor. $$15 y^{2}-2 x y^{2}-x^{2} y^{2}$$

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Key Concepts

Common Factor Extraction

This concept involves identifying and removing a common factor that is present in every term of an expression. In many algebraic expressions, factoring out a common monomial simplifies the problem and often reveals additional factoring opportunities.

Polynomial Factorization

After extracting any common factors, the next step is to factor the remaining polynomial, typically by rewriting it in standard quadratic form. Recognizing patterns such as quadratics allows one to express the polynomial as a product of simpler binomials, which is a key technique in simplifying algebraic expressions.

Quadratic Factoring Techniques

When the reduced expression is a quadratic, standard methods such as splitting the middle term, factor-by-grouping, or using the quadratic formula can be employed to factor it. Identifying two numbers that multiply to the constant term and add to the coefficient of the linear term is often a crucial step in this process.

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