/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 53 Factor each perfect square trino... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 53

Factor each perfect square trinomial. $$4 x^{2}+4 x+1$$

Short Answer

Expert verified
The factored form of the given perfect square trinomial is \((2x + 1)^{2}\).

Step by step solution

01

Identify the terms in trinomial

Firstly, identify the constants \(a\), \(b\) and \(c\) in the given trinomial \(ax^{2} + 2abx + b^{2}\). Here, we can see for the equation \(4x^{2} + 4x + 1\), \(a = 2x\), \(b = 1\), and \(c = 1\).
02

Check if the trinomial is a perfect square

Now, check if the trinomial is a perfect square. A trinomial \(ax^{2} + 2abx + b^{2}\) is a perfect square if \(2ab = 2 * a * b\). Here, \(2ab = 2 * 2x * 1 = 4x\), which is indeed our middle term. Hence, the trinomial is a perfect square trinomial.
03

Factor the perfect square trinomial

The perfect square trinomial takes the form \((ax + b)^{2}\) or \((ax - b)^{2}\). Since our middle term is positive, we will use the '+'. Replace \(a\) and \(b\) with the specific values from step 1 to get the factored form of the trinomial. Thus, our factored trinomial is \((2x + 1)^{2}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. An elevator at a construction site has a maximum capacity of 3000 pounds. If the elevator operator weighs 245 pounds and each cement bag weighs 95 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

Will help you prepare for the material covered in the next section. A telephone texting plan has a monthly fee of \(\$ 20\) with a charge of \(\$ 0.05\) per text. Write an algebraic expression that models the plan's monthly cost for \(x\) text messages.

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x^{2},\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3

Explain how to find the least common denominator for denominators of \(x^{2}-100\) and \(x^{2}-20 x+100\).

Explain how to add rational expressions having no common factors in their denominators. Use \(\frac{3}{x+5}+\frac{7}{x+2}\) in your explanation.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.