/*! 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 56 Find each product. $$(x-1)^{3}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 56

Find each product. $$(x-1)^{3}$$

Short Answer

Expert verified
The product of \( (x-1)^3 \) is \( x^3 - 3x^2 + 3x - 1 \).

Step by step solution

01

Understand the Binomial Theorem

The Binomial Theorem tells us how to expand expressions of the form \( (a + b)^n \), where \( n \) is a natural number. For \( (x - 1)^3 \), this means expanding out \( (x - 1)(x - 1)(x - 1) \).
02

Perform Multiplication

Start by multiplying the first two expressions, \( (x - 1)(x - 1) \), and then, multiply the result by the third expression. Therefore, done incrementally: First, \( (x - 1)(x - 1) = x^2 - 2x + 1 \), then we multiply this by \( (x - 1) \), which gives \( (x^2 - 2x + 1)(x - 1) \).
03

Distribution of terms

Distribute terms by multiplying each term in the expression \( (x^2 -2x +1) \) by \( (x-1) \). This gives us \( x^3 - 2x^2 + x - x^2 + 2x - 1 = x^3 - 3x^2 + 3x - 1 \).

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

What difference is there in simplifying \(\sqrt[3]{(-5)^{3}}\) and \(\sqrt[4]{(-5)^{4}} ?\)

Simplify using properties of exponents. $$\left(125 x^{9} y^{6}\right)^{3}$$

Explain how to factor \(x^{3}+1\)

Why must \(a\) and \(b\) represent non negative numbers when we write \(\sqrt{a} \cdot \sqrt{b}=\sqrt{a b ?}\) Is it necessary to use this restriction in the case of \(\sqrt[3]{a} \cdot \sqrt[3]{b}=\sqrt[3]{a b} ?\) Explain.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Special-product formulas have patterns that make their multiplications quicker than using the FOIL method.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Statistics

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.