Algebra: Structure And Method, Book 1
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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Chapter 6.1, Problem 41WE
To determine

To calculate: The simplified form of the expression 25x236y210x2+3xy18y2 and state restrictions on variable.

Expert Solution & Answer
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Answer to Problem 41WE

The simplified value of the expression 25x236y210x2+3xy18y2 is 5x+6y2x+3y and restriction is x3y2,x6y5.

Explanation of Solution

Given information:

The expression 25x236y210x2+3xy18y2.

Formula used:

The simplest form of an algebraic fraction is when numerator and denominator have no common factor other than 1 and 1 . Simplification is done by factorizing numerator and denominator.

Calculation:

Consider the expression 25x236y210x2+3xy18y2.

Recall that the simplest form of an algebraic fraction is when numerator and denominator have no common factor other than 1 and 1 . Simplification is done by factorizing numerator and denominator.

So, factorize numerator using the formula X2Y2=(X+Y)(XY) and denominator using the middle term splitting method and then strike out common terms from the expression and simplify it as,

  25x236y210x2+3xy18y2=(5x)2(6y)210x2+15xy12xy18y2=(5x+6y)(5x6y)5x(2x+3y)6y(2x+3y)=(5x+6y)(5x6y)(2x+3y)(5x6y)=5x+6y2x+3y

To restrict the variable, exclude the value that makes the denominator zero.

So, denominator will be zero when,

  (2x+3y)(5x6y)=02x+3y=0,5x6y=02x=3y,5x=6yx=3y2,x=6y5

For denominator not to be zero, x3y2,x6y5 .

Thus, the simplified value of the expression 25x236y210x2+3xy18y2 is 5x+3y2x+3y and restriction is x3y2,x6y5.

Chapter 6 Solutions

Algebra: Structure And Method, Book 1

Ch. 6.1 - Prob. 11OECh. 6.1 - Prob. 12OECh. 6.1 - Prob. 13OECh. 6.1 - Prob. 14OECh. 6.1 - Prob. 15OECh. 6.1 - Prob. 16OECh. 6.1 - Prob. 1WECh. 6.1 - Prob. 2WECh. 6.1 - Prob. 3WECh. 6.1 - Prob. 4WECh. 6.1 - Prob. 5WECh. 6.1 - Prob. 6WECh. 6.1 - Prob. 7WECh. 6.1 - Prob. 8WECh. 6.1 - Prob. 9WECh. 6.1 - Prob. 10WECh. 6.1 - Prob. 11WECh. 6.1 - Prob. 12WECh. 6.1 - Prob. 13WECh. 6.1 - Prob. 14WECh. 6.1 - Prob. 15WECh. 6.1 - Prob. 16WECh. 6.1 - Prob. 17WECh. 6.1 - Prob. 18WECh. 6.1 - Prob. 19WECh. 6.1 - Prob. 20WECh. 6.1 - Prob. 21WECh. 6.1 - Prob. 22WECh. 6.1 - Prob. 23WECh. 6.1 - Prob. 24WECh. 6.1 - Prob. 25WECh. 6.1 - Prob. 26WECh. 6.1 - Prob. 27WECh. 6.1 - Prob. 28WECh. 6.1 - Prob. 29WECh. 6.1 - Prob. 30WECh. 6.1 - Prob. 31WECh. 6.1 - Prob. 32WECh. 6.1 - Prob. 33WECh. 6.1 - Prob. 34WECh. 6.1 - Prob. 35WECh. 6.1 - Prob. 36WECh. 6.1 - Prob. 37WECh. 6.1 - Prob. 38WECh. 6.1 - Prob. 39WECh. 6.1 - Prob. 40WECh. 6.1 - Prob. 41WECh. 6.1 - Prob. 42WECh. 6.1 - Prob. 43WECh. 6.1 - Prob. 44WECh. 6.1 - 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Prob. 5MRECh. 6.4 - Prob. 6MRECh. 6.4 - Prob. 7MRECh. 6.4 - Prob. 8MRECh. 6.4 - Prob. 9MRECh. 6.4 - Prob. 10MRECh. 6.4 - Prob. 11MRECh. 6.4 - Prob. 12MRECh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.5 - Prob. 1OECh. 6.5 - Prob. 2OECh. 6.5 - Prob. 3OECh. 6.5 - Prob. 4OECh. 6.5 - Prob. 5OECh. 6.5 - Prob. 6OECh. 6.5 - Prob. 7OECh. 6.5 - Prob. 8OECh. 6.5 - Prob. 9OECh. 6.5 - Prob. 10OECh. 6.5 - Prob. 11OECh. 6.5 - Prob. 12OECh. 6.5 - Prob. 13OECh. 6.5 - Prob. 14OECh. 6.5 - Prob. 15OECh. 6.5 - Prob. 16OECh. 6.5 - Prob. 17OECh. 6.5 - Prob. 18OECh. 6.5 - Prob. 19OECh. 6.5 - Prob. 20OECh. 6.5 - Prob. 1WECh. 6.5 - Prob. 2WECh. 6.5 - Prob. 3WECh. 6.5 - Prob. 4WECh. 6.5 - Prob. 5WECh. 6.5 - Prob. 6WECh. 6.5 - Prob. 7WECh. 6.5 - Prob. 8WECh. 6.5 - Prob. 9WECh. 6.5 - Prob. 10WECh. 6.5 - Prob. 11WECh. 6.5 - Prob. 12WECh. 6.5 - Prob. 13WECh. 6.5 - Prob. 14WECh. 6.5 - Prob. 15WECh. 6.5 - Prob. 16WECh. 6.5 - Prob. 17WECh. 6.5 - Prob. 18WECh. 6.5 - Prob. 19WECh. 6.5 - Prob. 20WECh. 6.5 - Prob. 21WECh. 6.5 - Prob. 22WECh. 6.5 - Prob. 23WECh. 6.5 - Prob. 24WECh. 6.5 - Prob. 25WECh. 6.5 - Prob. 26WECh. 6.5 - Prob. 27WECh. 6.5 - Prob. 28WECh. 6.5 - Prob. 29WECh. 6.5 - Prob. 30WECh. 6.5 - Prob. 31WECh. 6.5 - Prob. 32WECh. 6.5 - Prob. 33WECh. 6.5 - Prob. 34WECh. 6.5 - Prob. 35WECh. 6.5 - Prob. 36WECh. 6.5 - Prob. 37WECh. 6.5 - Prob. 38WECh. 6.5 - Prob. 39WECh. 6.5 - Prob. 40WECh. 6.5 - Prob. 41WECh. 6.5 - Prob. 42WECh. 6.5 - Prob. 43WECh. 6.5 - Prob. 44WECh. 6.5 - Prob. 45WECh. 6.5 - Prob. 46WECh. 6.5 - Prob. 47WECh. 6.5 - Prob. 48WECh. 6.5 - Prob. 49WECh. 6.5 - Prob. 50WECh. 6.5 - Prob. 51WECh. 6.5 - Prob. 52WECh. 6.5 - Prob. 53WECh. 6.5 - Prob. 54WECh. 6.5 - Prob. 55WECh. 6.5 - Prob. 56WECh. 6.5 - Prob. 57WECh. 6.5 - Prob. 58WECh. 6.5 - Prob. 1MRECh. 6.5 - Prob. 2MRECh. 6.5 - 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