/*! 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 40 Multiply. $$ (a-0.4)(a-0.8) ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 40

Multiply. $$ (a-0.4)(a-0.8) $$

Short Answer

Expert verified
a^2 - 1.2a + 0.32

Step by step solution

01

- Apply the distributive property

Use the distributive property to multiply each term in the first parenthesis by each term in the second parenthesis. \[(a-0.4)(a-0.8) = a(a-0.8) - 0.4(a-0.8)\]
02

- Perform the multiplications

Multiply each term accordingly: \[a(a-0.8) = a^2 - 0.8a\] \[-0.4(a-0.8) = -0.4a + 0.32\]
03

- Combine like terms

Add the results from Step 2 together to combine like terms: \[a^2 - 0.8a - 0.4a + 0.32\] Combine the terms involving \(a\): \[a^2 - 1.2a + 0.32\]

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.

Distributive Property
The distributive property is a key concept in algebra that allows you to multiply a single term by each term inside a parenthesis. It's like distributing the single term across the terms in the parenthesis.
For our example, let鈥檚 multiply \((a-0.4)(a-0.8)\).
We distribute each term in the first parenthesis to each term in the second parenthesis.
  • First term: \(a \cdot (a-0.8)\) which gives \(a^2 - 0.8a\)
  • Second term: \(-0.4 \cdot (a-0.8)\) which gives \(-0.4a + 0.32\)
After the distribution, we move to the next step, combining like terms, to simplify the expression further.
Combining Like Terms
Combining like terms is the process of simplifying an expression by merging terms that have the same variables raised to the same power. This simplifies the expression and makes it easier to understand.
From our distribution step, we have: \(a^2 - 0.8a - 0.4a + 0.32\).
Identify like terms:
  • Like terms with \(a\): \-0.8a and -0.4a
We add them together to get:
\(a^2 - 1.2a + 0.32\).
Combining like terms ensures our equation is as simple as possible.
Multiplying Binomials
Multiplying binomials combines the distributive property and combining like terms. A binomial is an algebraic expression containing two terms. When we multiply two binomials, we use the distributive property multiple times.
In our example, \((a-0.4)(a-0.8)\), we start by distributing each term in the first binomial:
  • \(a \cdot (a-0.8)\) results in \(a^2 - 0.8a\)
  • \(-0.4 \cdot (a-0.8)\) results in \(-0.4a + 0.32\)
Then, we combine the like terms:
\(a^2 - 0.8a - 0.4a + 0.32\) simplifies to \(a^2 - 1.2a + 0.32\).
Understanding how to multiply binomials allows us to handle more complex polynomial operations easily.

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

Write \(\frac{4}{32}\) in decimal notation, simplified fraction notation, and scientific notation.

Find the domain of \(f / g,\) if $$ f(x)=\frac{3 x}{2 x+5} \quad \text { and } \quad g(x)=\frac{x^{4}-1}{3 x+9} $$

For each pair of functions \(f\) and \(g,\) determine the domain of \(f / g\) $$ \begin{aligned} &f(x)=\frac{2 x}{x+1}\\\ &g(x)=2 x+5 \end{aligned} $$

Construct three like terms of degree 4.

Use the fact that \(10^{3} \approx 2^{10}\) to estimate each of the following powers of \(2 .\) Then compute the power of 2 with a calculator and find the difference between the exact value and the approximation. $$ 2^{22} $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics 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.