1. Alisha and David were working on cubing binomials (raising binomials to the third power) for their math homework. Alisha believed they could save time with a shortcut. She wrote the rule below for David to follow. Rule: (a+ b) = a' +b Does Alisha's shortcut always work? Justify your result algebraically.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Alisha and David were working on cubing binomials (raising binomials to the third power)
for their math homework. Alisha believed they could save time with a shortcut. She wrote
the rule below for David to follow.
Rule: (a+ b) = a' +b
Does Alisha's shortcut always work? Justify your result algebraically.
Transcribed Image Text:1. Alisha and David were working on cubing binomials (raising binomials to the third power) for their math homework. Alisha believed they could save time with a shortcut. She wrote the rule below for David to follow. Rule: (a+ b) = a' +b Does Alisha's shortcut always work? Justify your result algebraically.
Expert Solution
Step 1

Formula used:

a+b3=a3+b3+3a2b+3b2a

calculation:

It is observed that shortcut rule that is used by person A  is not always right, because the formula for a+b3=a3+b3+3a2b+3b2a.

Simplify the shortcut rule for person A is as follows:

a3+b3+3a2b+3ab2=a3+b33a2b+3ab2=03aba+b=0

 

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