Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba…

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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Question

Chapter 5.7, Problem 4ST

To determine

To simplify the given expression.

Expert Solution & Answer

Answer to Problem 4ST

Explanation of Solution

Given:

Expression: 2u2+3uv−2v22u2−3uv−2v2⋅2u+v2u−v

Concept used:

To simplify the given expression:

Find the Least Common Multiple of the fraction and write in reduced form.
Take out common terms in the given expression.
Cancel out the terms that are in common in numerator and the denominator.
Find if any algebraic identities can simplify the given expression.

Calculation:

Using the above concept,

⇒2u2+3uv−2v22u2−3uv−2v2⋅2u+v2u−v⇒(2u2+3uv−2v2)(2u+v)(2u2−3uv−2v2)(2u−v)

Factorize the numerator.

⇒2u2+3uv−2v2⇒2u2−uv+4uv−2v2⇒(2u2−uv)+(4uv−2v2)⇒u(2u−v)−2v(2u−v)⇒(u−2v)(2u−v)

Factorize the denominator,

⇒2u2−3uv−2v2⇒2u2+uv−4uv−2v2⇒(2u2+uv)−(4uv+2v2)⇒u(2u+v)−2v(2u+v)⇒(u−2v)(2u+v)

Substituting in the given expression,

⇒(u−2v)(2u−v)(2u+v)(u−2v)(2u+v)(2u−v)⇒(u−2v)(2u−v)(2u+v)(u−2v)(2u+v)(2u−v)⇒11⇒1

Conclusion:

Therefore, the simplified form of the expression is 1.

Chapter 5.7, Problem 3ST

Chapter 5.7, Problem 5ST

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 1OE Ch. 5.1 - Prob. 2OE Ch. 5.1 - Prob. 3OE Ch. 5.1 - Prob. 4OE Ch. 5.1 - Prob. 5OE Ch. 5.1 - Prob. 6OE Ch. 5.1 - Prob. 7OE Ch. 5.1 - Prob. 8OE Ch. 5.1 - Prob. 9OE Ch. 5.1 - Prob. 10OE

Ch. 5.1 - Prob. 11OE Ch. 5.1 - Prob. 12OE Ch. 5.1 - Prob. 1WE Ch. 5.1 - Prob. 2WE Ch. 5.1 - Prob. 3WE Ch. 5.1 - Prob. 4WE Ch. 5.1 - Prob. 5WE Ch. 5.1 - Prob. 6WE Ch. 5.1 - Prob. 7WE Ch. 5.1 - Prob. 8WE Ch. 5.1 - Prob. 9WE Ch. 5.1 - Prob. 10WE Ch. 5.1 - Prob. 11WE Ch. 5.1 - Prob. 12WE Ch. 5.1 - Prob. 13WE Ch. 5.1 - Prob. 14WE Ch. 5.1 - Prob. 15WE Ch. 5.1 - Prob. 16WE Ch. 5.1 - Prob. 17WE Ch. 5.1 - Prob. 18WE Ch. 5.1 - Prob. 19WE Ch. 5.1 - Prob. 20WE Ch. 5.1 - Prob. 21WE Ch. 5.1 - Prob. 22WE Ch. 5.1 - Prob. 23WE Ch. 5.1 - Prob. 24WE Ch. 5.1 - Prob. 25WE Ch. 5.1 - Prob. 26WE Ch. 5.1 - Prob. 27WE Ch. 5.1 - Prob. 28WE Ch. 5.1 - Prob. 29WE Ch. 5.1 - Prob. 30WE Ch. 5.1 - Prob. 31WE Ch. 5.1 - Prob. 32WE Ch. 5.1 - Prob. 33WE Ch. 5.1 - Prob. 34WE Ch. 5.1 - Prob. 35WE Ch. 5.1 - Prob. 36WE Ch. 5.1 - Prob. 1MRE Ch. 5.1 - Prob. 2MRE Ch. 5.1 - Prob. 3MRE Ch. 5.1 - Prob. 4MRE Ch. 5.1 - Prob. 5MRE Ch. 5.1 - Prob. 6MRE Ch. 5.1 - Prob. 7MRE Ch. 5.1 - Prob. 8MRE Ch. 5.1 - Prob. 9MRE Ch. 5.1 - Prob. 10MRE Ch. 5.1 - 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