step 1 In this problem, we're being asked to square the trinomial x squared minus 2x plus 1. Now, we do

Question

$\left(x^{2}-2 x+1\right)^{2}$

Name: Problem 19, Chapter 0: Finite Mathematics and Applied Calculus
Uploaded: 2021-09-22T21:44:04-08:00
Duration: 1 min 40 s
Channel: Julie Silva
Description: (x^2-2 x+1)^2

   $\left(x^{2}-2 x+1\right)^{2}$

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 0, Problem 19

Instant Answer

Solved by Expert Julie Silva

09/22/2021

Step 1

Step 1: First, we write down the expression twice, because squaring means multiplying the expression by itself: \[(x^{2}-2x+1)^{2} = (x^{2}-2x+1)(x^{2}-2x+1)\] Show more…

Show all steps

Thanks for your feedback!

$\left(x^{2}-2 x+1\right)^{2}$

Play audio

Feedback

Julie Silva and 56 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Perfect Square Trinomial

A perfect square trinomial is a quadratic expression that can be written as the square of a binomial. In this case, the expression x² - 2x + 1 fits the pattern a² - 2ab + b², which factors into (x - 1)². Recognizing perfect square trinomials simplifies the process of factoring or further manipulating expressions, as it reduces a quadratic to a simpler binomial form, which can be useful for solving equations or evaluating expressions.

Exponentiation Rules

Exponentiation rules, such as the power of a power rule, state that when an expression with an exponent is raised to another power, you multiply the exponents. In the given problem, after recognizing that x² - 2x + 1 equals (x - 1)², raising it to the second power means applying the rule ((x - 1)²)² = (x - 1)^(2×2) = (x - 1)^4. This concept is fundamental in algebra as it facilitates the simplification and expansion of expressions involving exponents.

Please give Ace some feedback