Question

Factor by grouping. $$ m p-n p-m q+n q $$

   Factor by grouping.
$$
m p-n p-m q+n q
$$

Elementary and Intermediate Algebra

Elementary and Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 6, Problem 91

Instant Answer

Solved by Expert Amy Jiang

04/15/2020

Step 1

So, we group the terms accordingly. $$ mp - np - mq + nq = (mp - np) - (mq - nq) $$ Show more…

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Factor by grouping. $$ m p-n p-m q+n q $$

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Key Concepts

Polynomial Factoring

Polynomial factoring is the process of breaking down a polynomial into a product of simpler polynomials. This technique is important not only for simplification but also for solving equations, as it reveals the zeros and overall structure of the polynomial.

Distributive Property

The distributive property allows multiplication to be distributed over addition. In the context of factoring, it is used both to combine and separate terms, helping to factor out common factors and rewrite the expression in a simplified, factored form.

Common Factor

A common factor in an expression is a term or variable that divides each term. Identifying and extracting common factors simplifies an expression significantly and is an essential step in many factoring techniques, including grouping.

Factor by Grouping

Factor by grouping is a method for factoring polynomials, typically useful when dealing with expressions with four or more terms. This method involves splitting the expression into groups that have common factors, then factoring out these common elements and further factoring the resulting expression.

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