/*! 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 74 Use a calculator to help find ea... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 74

Use a calculator to help find each product. $$ (-0.31 x+29.3)(-0.31 x-29.3) $$

Short Answer

Expert verified
The product is \(0.0961x^2 - 857.49\).

Step by step solution

01

Identify the Formula

This expression is in the form \((a+b)(a-b)\). This is known as the difference of squares, and it simplifies to \(a^2 - b^2\). Recognize that \(a = -0.31x\) and \(b = 29.3\).
02

Apply the Difference of Squares Formula

Using the difference of squares, we calculate \(a^2 = (-0.31x)^2\) and \(b^2 = (29.3)^2\). The expression simplifies to \((-0.31x)^2 - (29.3)^2\).
03

Calculate Each Square

Calculate \((-0.31x)^2 = (0.31)^2x^2 = 0.0961x^2\) and \((29.3)^2 = 857.49\). Use a calculator for precise calculation of these squares.
04

Substitute Values and Simplify

Substitute the calculated squares back into the expression to get \(0.0961x^2 - 857.49\). This is the fully simplified expression representing the product of the two binomials.

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.

Polynomial Multiplication
Polynomial multiplication involves combining two or more polynomials to generate a new polynomial. This process requires you to apply operations like distribution, sometimes over multiple terms, and can involve special formulas. In the exercise
  • Each binomial is written in the form of \((a + b)(a - b)\), a common structure in algebra known as the "difference of squares."
  • This special case makes it easier because we do not have to multiply every term by every other term, but simply apply the formula.
The result of this effect is a significant simplification: \[ a^2 - b^2 \]where you multiply the terms from each polynomial according to specified rules.
Algebraic Expressions
Algebraic expressions are combinations of variables, numbers, and operation symbols. They can represent real-world situations, and you work with them to find values or simplify calculations.
  • In our exercise, you'll see terms like \(-0.31x\) and \(29.3\).
  • These expressions are manipulated using mathematical operations like factoring or expanding.
Variables such as \(x\) make the expressions dynamic and adaptable, as these letters stand for numbers we may want to explore. The numerical coefficients like \(-0.31\) show the fixed amount that the variable is multiplied by, allowing one to predict or determine exact values in broader contexts.
Simplifying Expressions
Simplifying expressions is the process of making them easier to work with or understand. It often involves reducing them to the simplest form by applying known techniques or operations.
  • For difference of squares, this means substituting the calculated powers into the template \(a^2 - b^2\).
  • The exercise demonstrates simplifying from \((-0.31x)^2 - (29.3)^2\) to \(0.0961x^2 - 857.49\).
Simplification helps in making expressions usable for further calculations and is an essential skill in algebra. This technique aids in reducing complexity and providing clear, concise answers that can be easily interpreted.

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. Assume all variables represent natural numbers. $$ a^{3 b}-c^{3 b} $$

The surface area of a cubical block of ice is represented by the polynomial \(6 x^{2}+36 x+54 .\) Use factoring to find an expression that represents the length of an edge of the block.

The area of a square checkerboard is represented by the polynomial \(25 x^{2}-40 x+16 .\) Use factoring to find an expression that represents the length of a side. (IMAGE CANT COPY)

Find the domain of the function defined by: $$ f(x)=\frac{3}{x^{2}-x-6} $$

Construct a table of values for each polynomial function using the given values for \(x .\) Then graph the function and find its domain and range. $$ \begin{aligned} &f(x)=-x^{2}+2 x+6\\\ &x=-2,-1,0,1,2,3,4 \end{aligned} $$ $$ \begin{array}{|r|l|} \hline x & f(x) \\ \hline-2 & \\ -1 & \\ 0 & \\ 1 & \\ 2 & \\ 3 & \\ 4 & \\ \hline \end{array} $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

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.