Question

Factor each polynomial. $(m-n)^{2}+4(m-n)+4$

   Factor each polynomial.
$(m-n)^{2}+4(m-n)+4$

Intermediate Algebra

Intermediate Algebra

John Hornsby; Terry… 13th Edition

Chapter 5, Problem 36

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Solved by Expert Vamshi. 7Fs

02/27/2022

Step 1

Step 1: First, we can rewrite the given polynomial $(m-n)^{2}+4(m-n)+4$ in the form of $a^2 + 2ab + b^2$ which is the expanded form of $(a+b)^2$. Show more…

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Factor each polynomial. $(m-n)^{2}+4(m-n)+4$

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Key Concepts

Polynomial Factoring

Polynomial factoring is the process of rewriting a polynomial as a product of simpler polynomial factors. It is a fundamental technique used to simplify expressions, solve polynomial equations, and analyze polynomial functions.

Substitution Method

The substitution method involves replacing a part of the expression with a new variable to simplify the problem. In the context of factoring, it helps in transforming complex expressions into a simpler form, often revealing standard factoring patterns that are not immediately obvious.

Perfect Square Trinomial

A perfect square trinomial is a quadratic expression that can be written as the square of a binomial. It has the form a^2 + 2ab + b^2, which factors directly into (a + b)^2. Recognizing this pattern simplifies the factoring process greatly.

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