Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Concept explainers

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

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Question

Chapter 5.5, Problem 24WE

To determine

To simplify the given expression.

Expert Solution & Answer

Answer to Problem 24WE

(u4+u2v2+v4)(u2+uv+v2)(u2−uv+v2)

Explanation of Solution

Given:

Expression: (u4+u2v2+v4)÷(u6−v6)⋅(u2−v2)

Concept used:

To multiply two fractions, simply multiply numerators by each other and denominators by each other and then reduce the fraction if possible.

ab⋅cd→a×cb×d

To divide two fractions, simply flip the second fraction into a reciprocal and change the division sign to a multiplication sign and then multiply the two fractions by multiplying the numerators by each other and denominators by each other. As illustrated below:

ab÷cd→ab×dc→a×db×c

Formula used:

a2−b2=(a−b)(a+b)

(x3−y3)=(x−y)(x2+xy+y2)(x3+y3)=(x+y)(x2−xy+y2)

Calculation:

Consider the given expression,

⇒(u4+u2v2+v4)×1((u3)2−(v3)2)×(u2−v2) [Factorizing the fractions]

⇒(u4+u2v2+v4)×1(u3−v3)(u3+v3)×(u2−v2) [ ∵a2−b2=(a−b)(a+b) ]

⇒(u4+u2v2+v4)×1(u−v)(u2+uv+v2)(u+v)(u2−uv+v2)×(u−v)(u+v) [∵(x3−y3)=(x−y)(x2+xy+y2) (x3+y3)=(x+y)(x2−xy+y2)]

⇒(u4+u2v2+v4)×1(u2+uv+v2)(u2−uv+v2) [Reducing the fractions]

⇒(u4+u2v2+v4)(u2+uv+v2)(u2−uv+v2)

Conclusion:

Therefore, after simplification, the answer is (u4+u2v2+v4)(u2+uv+v2)(u2−uv+v2) .

Chapter 5.5, Problem 23WE

Chapter 5.5, Problem 1MRE

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

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