Answer 3 p 2 + 4 q 2 − 2 p 2 q − q 2 = p 2 ( 3 − q ) + 3 q 2 Explanation Given: 3 p 2 + 4 q 2 − 2 p 2 q − q 2 Concept Used: If an expression contains more than one operation between its terms and brackets, first solve the terms inside brackets and then apply division followed by multiplication, addition and subtraction. Calculation: To simplify the expression 3 p 2 + 4 q 2 − 2 p 2 q − q 2 First, group like terms together. As, 3 p 2 + 4 q 2 − 2 p 2 q − q 2 = 3 p 2 − 2 p 2 q + 4 q 2 − q 2 = 3 p 2 − 2 p 2 q + ( 4 − 1 ) q 2 = 3 p 2 − 2 p 2 q + 3 q 2 Now, take p 2 common from first two terms, as 3 p 2 − 2 p 2 q + 3 q 2 = p 2 ( 3 − q ) + 3 q 2 Now, above expression can’t be simplified further. Thus, simplified form of given expression is 3 p 2 + 4 q 2 − 2 p 2 q − q 2 = p 2 ( 3 − q ) + 3 q 2

(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 4.3, Problem 3MRE

To determine

To simplify the expression

$3p2+4q2−2p2q−q2$

Expert Solution & Answer

Answer to Problem 3MRE

$3p2+4q2−2p2q−q2=p2(3−q)+3q2$

Explanation of Solution

Given:

$3p2+4q2−2p2q−q2$

Concept Used:

If an expression contains more than one operation between its terms and brackets, first solve the terms inside brackets and then apply division followed by multiplication, addition and subtraction.

Calculation:

To simplify the expression

$3p2+4q2−2p2q−q2$

First, group like terms together.

As,

$3p2+4q2−2p2q−q2=3p2−2p2q+4q2−q2=3p2−2p2q+(4−1)q2=3p2−2p2q+3q2$

Now, take $p2$ common from first two terms, as

$3p2−2p2q+3q2=p2(3−q)+3q2$

Now, above expression can’t be simplified further.

Thus, simplified form of given expression is

$3p2+4q2−2p2q−q2=p2(3−q)+3q2$

Chapter 4.3, Problem 2MRE

Chapter 4.3, Problem 4MRE

Chapter 4 Solutions

Algebra: Structure And Method, Book 1

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Prob. 18WE Ch. 4.7 - Prob. 19WE Ch. 4.7 - Prob. 20WE Ch. 4.7 - Prob. 21WE Ch. 4.7 - Prob. 22WE Ch. 4.7 - Prob. 23WE Ch. 4.7 - Prob. 24WE Ch. 4.7 - Prob. 25WE Ch. 4.7 - Prob. 26WE Ch. 4.7 - Prob. 27WE Ch. 4.7 - Prob. 28WE Ch. 4.7 - Prob. 29WE Ch. 4.7 - Prob. 1MRE Ch. 4.7 - Prob. 2MRE Ch. 4.7 - Prob. 3MRE Ch. 4.7 - Prob. 4MRE Ch. 4.7 - Prob. 5MRE Ch. 4.7 - Prob. 6MRE Ch. 4.7 - Prob. 7MRE Ch. 4.7 - Prob. 8MRE Ch. 4.8 - Prob. 1OE Ch. 4.8 - Prob. 2OE Ch. 4.8 - Prob. 3OE Ch. 4.8 - Prob. 4OE Ch. 4.8 - Prob. 1P Ch. 4.8 - Prob. 2P Ch. 4.8 - Prob. 3P Ch. 4.8 - Prob. 4P Ch. 4.8 - Prob. 5P Ch. 4.8 - Prob. 6P Ch. 4.8 - Prob. 7P Ch. 4.8 - Prob. 8P Ch. 4.8 - Prob. 9P Ch. 4.8 - Prob. 10P Ch. 4.8 - Prob. 11P Ch. 4.8 - Prob. 12P Ch. 4.8 - Prob. 13P Ch. 4.8 - Prob. 14P Ch. 4.8 - Prob. 15P Ch. 4.8 - Prob. 16P Ch. 4.8 - Prob. 17P Ch. 4.8 - Prob. 18P Ch. 4.8 - Prob. 19P Ch. 4.8 - Prob. 20P Ch. 4.8 - Prob. 1MRE Ch. 4.8 - Prob. 2MRE Ch. 4.8 - Prob. 3MRE Ch. 4.8 - Prob. 4MRE Ch. 4.8 - Prob. 5MRE Ch. 4.8 - Prob. 6MRE Ch. 4.8 - Prob. 7MRE Ch. 4.8 - Prob. 8MRE Ch. 4.9 - Prob. 1OE Ch. 4.9 - Prob. 2OE Ch. 4.9 - Prob. 1P Ch. 4.9 - Prob. 2P Ch. 4.9 - Prob. 3P Ch. 4.9 - Prob. 4P Ch. 4.9 - Prob. 5P Ch. 4.9 - Prob. 6P Ch. 4.9 - Prob. 7P Ch. 4.9 - Prob. 8P Ch. 4.9 - Prob. 9P Ch. 4.9 - Prob. 10P Ch. 4.9 - Prob. 11P Ch. 4.9 - Prob. 12P Ch. 4.9 - Prob. 13P Ch. 4.9 - Prob. 1MRE Ch. 4.9 - Prob. 2MRE Ch. 4.9 - Prob. 3MRE Ch. 4.9 - Prob. 4MRE Ch. 4.9 - Prob. 5MRE Ch. 4.9 - Prob. 6MRE Ch. 4.9 - Prob. 7MRE Ch. 4.9 - Prob. 8MRE Ch. 4.9 - Prob. 9MRE Ch. 4.9 - Prob. 10MRE Ch. 4.9 - Prob. 11MRE Ch. 4.9 - Prob. 12MRE Ch. 4.10 - Prob. 1P Ch. 4.10 - Prob. 2P Ch. 4.10 - Prob. 3P Ch. 4.10 - Prob. 4P Ch. 4.10 - Prob. 5P Ch. 4.10 - Prob. 6P Ch. 4.10 - Prob. 7P Ch. 4.10 - Prob. 8P Ch. 4.10 - Prob. 9P Ch. 4.10 - Prob. 10P Ch. 4.10 - Prob. 11P Ch. 4.10 - Prob. 12P Ch. 4.10 - Prob. 13P Ch. 4.10 - Prob. 14P Ch. 4.10 - Prob. 15P Ch. 4.10 - Prob. 16P Ch. 4.10 - Prob. 1ST Ch. 4.10 - Prob. 2ST Ch. 4.10 - Prob. 3ST Ch. 4.10 - Prob. 4ST Ch. 4 - Prob. 1CR Ch. 4 - Prob. 2CR Ch. 4 - Prob. 3CR Ch. 4 - Prob. 4CR Ch. 4 - Prob. 5CR Ch. 4 - Prob. 6CR Ch. 4 - Prob. 7CR Ch. 4 - Prob. 8CR Ch. 4 - Prob. 9CR Ch. 4 - Prob. 10CR Ch. 4 - Prob. 11CR Ch. 4 - Prob. 12CR Ch. 4 - Prob. 13CR Ch. 4 - Prob. 14CR Ch. 4 - Prob. 15CR Ch. 4 - Prob. 16CR Ch. 4 - Prob. 17CR Ch. 4 - Prob. 18CR Ch. 4 - Prob. 1CT Ch. 4 - Prob. 2CT Ch. 4 - Prob. 3CT Ch. 4 - Prob. 4CT Ch. 4 - Prob. 5CT Ch. 4 - Prob. 6CT Ch. 4 - Prob. 7CT Ch. 4 - Prob. 8CT Ch. 4 - Prob. 9CT Ch. 4 - Prob. 10CT Ch. 4 - Prob. 11CT Ch. 4 - Prob. 12CT Ch. 4 - Prob. 13CT Ch. 4 - Prob. 14CT Ch. 4 - Prob. 15CT Ch. 4 - Prob. 16CT Ch. 4 - Prob. 17CT Ch. 4 - Prob. 18CT Ch. 4 - Prob. 19CT Ch. 4 - Prob. 20CT Ch. 4 - Prob. 21CT Ch. 4 - Prob. 22CT Ch. 4 - Prob. 1CLR Ch. 4 - Prob. 2CLR Ch. 4 - Prob. 3CLR Ch. 4 - Prob. 4CLR Ch. 4 - Prob. 5CLR Ch. 4 - Prob. 6CLR Ch. 4 - Prob. 7CLR Ch. 4 - Prob. 8CLR Ch. 4 - Prob. 9CLR Ch. 4 - Prob. 10CLR Ch. 4 - Prob. 11CLR Ch. 4 - Prob. 12CLR Ch. 4 - Prob. 13CLR Ch. 4 - Prob. 14CLR Ch. 4 - Prob. 15CLR Ch. 4 - Prob. 16CLR Ch. 4 - Prob. 17CLR Ch. 4 - Prob. 18CLR Ch. 4 - Prob. 19CLR Ch. 4 - Prob. 20CLR Ch. 4 - Prob. 21CLR Ch. 4 - Prob. 22CLR Ch. 4 - Prob. 23CLR Ch. 4 - Prob. 24CLR Ch. 4 - Prob. 25CLR Ch. 4 - Prob. 26CLR Ch. 4 - Prob. 27CLR Ch. 4 - Prob. 28CLR Ch. 4 - Prob. 29CLR Ch. 4 - Prob. 30CLR Ch. 4 - Prob. 31CLR Ch. 4 - Prob. 32CLR Ch. 4 - Prob. 33CLR Ch. 4 - Prob. 34CLR Ch. 4 - Prob. 35CLR Ch. 4 - Prob. 36CLR Ch. 4 - Prob. 37CLR Ch. 4 - Prob. 38CLR Ch. 4 - Prob. 39CLR Ch. 4 - Prob. 40CLR Ch. 4 - Prob. 1MS Ch. 4 - Prob. 2MS Ch. 4 - Prob. 3MS Ch. 4 - Prob. 4MS Ch. 4 - Prob. 5MS Ch. 4 - Prob. 6MS Ch. 4 - Prob. 7MS Ch. 4 - Prob. 8MS Ch. 4 - Prob. 9MS Ch. 4 - Prob. 10MS Ch. 4 - Prob. 11MS Ch. 4 - Prob. 12MS Ch. 4 - Prob. 13MS Ch. 4 - Prob. 14MS Ch. 4 - Prob. 15MS Ch. 4 - Prob. 16MS Ch. 4 - Prob. 17MS Ch. 4 - Prob. 18MS Ch. 4 - Prob. 19MS Ch. 4 - Prob. 20MS Ch. 4 - Prob. 21MS Ch. 4 - Prob. 22MS Ch. 4 - Prob. 23MS Ch. 4 - Prob. 24MS Ch. 4 - Prob. 25MS Ch. 4 - Prob. 26MS Ch. 4 - Prob. 27MS Ch. 4 - Prob. 28MS Ch. 4 - Prob. 29MS Ch. 4 - Prob. 30MS Ch. 4 - Prob. 31MS

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