/*! 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 50 Find each product. $$(9-5 x)^{... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 50

Find each product. $$(9-5 x)^{2}$$

Short Answer

Expert verified
The squared result of (9 - 5x) is \(25x^2 - 90x + 81\).

Step by step solution

01

Identify the Binomial

The given expression is a binomial: (9 - 5x). We'll square this binomial.
02

Apply the Binomial Square Identity

Using the identity for the square of a binomial, \((a-b)^2 = a^2 - 2ab + b^2\), substitute \(a = 9\) and \(b = 5x\). We get \((9)^2 - 2*9*5x + (5x)^2\).
03

Simplify the Expression

Simplify the expression to get the final result. First calculate \(9^2\), then calculate \(2*9*5x\), and then \((5x)^2\). Adding these all together, we have \(81 - 90x + 25x^2\).

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Binomial Theorem
The Binomial Theorem is a powerful tool in algebra that allows us to expand binomials raised to any power efficiently. A binomial is an algebraic expression that contains two terms. When you see something like \[ (a + b)^n \], it indicates that we are looking to expand this into a polynomial using the binomial expansion formula. For squaring a binomial, like in our problem \[ (9 - 5x)^2 \], we can apply a specific identity from the theorem directly.
Algebraic Expression
An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. In our exercise, the binomial \[ (9 - 5x) \] is composed of numbers and a variable. Understanding the elements in an algebraic expression helps us rewrite and manipulate expressions correctly. In the expression "9 - 5x,"
  • 9 is a constant term, which does not change.
  • 5x is a term with a coefficient (5) and a variable (x).
Remember, when working with algebraic expressions, it's essential to recognize each part so that when applying formulas, each component is treated accurately.
Polynomial Simplification
Simplifying polynomials involves combining like terms and expressing the polynomial in its simplest form. After expanding a binomial, like \[ (9 - 5x)^2 \],we end up with a polynomial. In our case, \[ 81 - 90x + 25x^2 \].During simplification,
  • First, calculate individual parts, such as \(9^2\), \(2 \times 9 \times 5x\), and \((5x)^2\).
  • Then, combine all like terms if needed, although in this simple case, we do not have redundant terms.
The outcome is a neat and organized polynomial that clearly shows each component without extra unnecessary complexity.

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

Factor completely. $$x^{4}-y^{4}-2 x^{3} y+2 x y^{3}$$

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

List all numbers that must be excluded from the domain of each rational expression. $$\frac{3}{2 x^{2}+4 x-9}$$

Solve each equation. $$\sqrt{x+8}-\sqrt{x-4}=2$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{\sqrt{20}}{8}=\frac{\sqrt{10}}{4}$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Calculus

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.