Algebra: Structure And Method, Book 1

(REV)00 Edition

ISBN: 9780395977224

Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher: McDougal Littell

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Question

Chapter 6.2, Problem 58WE

To determine

To calculate: The simplified form of the expression a2−(b−c)22a−2b+2c⋅6a−6b+6cb2−(a−c)2.

Expert Solution & Answer

Answer to Problem 58WE

The simplified form of the expression a2−(b−c)22a−2b+2c⋅6a−6b+6cb2−(a−c)2 is 3(a−b+c)(b−a+c).

Explanation of Solution

Given information:

The expression a2−(b−c)22a−2b+2c⋅6a−6b+6cb2−(a−c)2.

Formula used:

Fractions are multiplied as ab⋅cd=abcd.

To factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

Calculation:

Consider the expression a2−(b−c)22a−2b+2c⋅6a−6b+6cb2−(a−c)2.

Recall that square of difference of two numbers a and bis (a−b)2=a2+b2−2ab.

Therefore,

a2−(b−c)22a−2b+2c⋅6a−6b+6cb2−(a−c)2=(a−b+c)(a+b−c)2a−2b+2c⋅6a−6b+6c(b−a+c)(b+a−c)=(a−b+c)(a+b−c)2(a−b+c)⋅6(a−b+c)(b−a+c)(b+a−c)

Strike off the similar terms,

a2−(b−c)22a−2b+2c⋅6a−6b+6cb2−(a−c)2=(a−b+c)(a+b−c)2a−2b+2c⋅6a−6b+6c(b−a+c)(b+a−c)=(a−b+c)(a+b−c)2(a−b+c)⋅6(a−b+c)(b−a+c)(b+a−c)=(a−b+c)1⋅3(b−a+c)

Recall that fractions are multiplied as ab⋅cd=abcd.

Apply it,

a2−(b−c)22a−2b+2c⋅6a−6b+6cb2−(a−c)2=(a−b+c)(a+b−c)2a−2b+2c⋅6a−6b+6c(b−a+c)(b+a−c)=(a−b+c)(a+b−c)2(a−b+c)⋅6(a−b+c)(b−a+c)(b+a−c)=(a−b+c)1⋅3(b−a+c)=3(a−b+c)(b−a+c)

Thus, the simplified form of the expression a2−(b−c)22a−2b+2c⋅6a−6b+6cb2−(a−c)2 is 3(a−b+c)(b−a+c).

Chapter 6.2, Problem 57WE

Chapter 6.2, Problem 59WE

Chapter 6 Solutions

Algebra: Structure And Method, Book 1

Ch. 6.1 - Prob. 1OE Ch. 6.1 - Prob. 2OE Ch. 6.1 - Prob. 3OE Ch. 6.1 - Prob. 4OE Ch. 6.1 - Prob. 5OE Ch. 6.1 - Prob. 6OE Ch. 6.1 - Prob. 7OE Ch. 6.1 - Prob. 8OE Ch. 6.1 - Prob. 9OE Ch. 6.1 - Prob. 10OE

Ch. 6.1 - Prob. 11OE Ch. 6.1 - Prob. 12OE Ch. 6.1 - Prob. 13OE Ch. 6.1 - Prob. 14OE Ch. 6.1 - Prob. 15OE Ch. 6.1 - Prob. 16OE Ch. 6.1 - Prob. 1WE Ch. 6.1 - Prob. 2WE Ch. 6.1 - Prob. 3WE Ch. 6.1 - Prob. 4WE Ch. 6.1 - Prob. 5WE Ch. 6.1 - Prob. 6WE Ch. 6.1 - Prob. 7WE Ch. 6.1 - Prob. 8WE Ch. 6.1 - Prob. 9WE Ch. 6.1 - Prob. 10WE Ch. 6.1 - Prob. 11WE Ch. 6.1 - Prob. 12WE Ch. 6.1 - Prob. 13WE Ch. 6.1 - Prob. 14WE Ch. 6.1 - Prob. 15WE Ch. 6.1 - Prob. 16WE Ch. 6.1 - Prob. 17WE Ch. 6.1 - Prob. 18WE Ch. 6.1 - Prob. 19WE Ch. 6.1 - Prob. 20WE Ch. 6.1 - Prob. 21WE Ch. 6.1 - Prob. 22WE Ch. 6.1 - Prob. 23WE Ch. 6.1 - Prob. 24WE Ch. 6.1 - Prob. 25WE Ch. 6.1 - Prob. 26WE Ch. 6.1 - Prob. 27WE Ch. 6.1 - Prob. 28WE Ch. 6.1 - Prob. 29WE Ch. 6.1 - Prob. 30WE Ch. 6.1 - Prob. 31WE Ch. 6.1 - Prob. 32WE Ch. 6.1 - Prob. 33WE Ch. 6.1 - Prob. 34WE Ch. 6.1 - Prob. 35WE Ch. 6.1 - Prob. 36WE Ch. 6.1 - Prob. 37WE Ch. 6.1 - Prob. 38WE Ch. 6.1 - Prob. 39WE Ch. 6.1 - Prob. 40WE Ch. 6.1 - Prob. 41WE Ch. 6.1 - Prob. 42WE Ch. 6.1 - 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To calculate: The simplified form of the expression a2−(b−c)22a−2b+2c⋅6a−6b+6cb2−(a−c)2.

Answer to Problem 58WE

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