Textbook Question
Write each number in decimal notation without the use of exponents.
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 74
In Exercises 67–82, find each product. (9x+7y)2
Verified step by step guidance1
Recognize that the expression \((9x + 7y)^2\) is a binomial squared. This means you will use the formula for the square of a binomial: \((a + b)^2 = a^2 + 2ab + b^2\).
Identify the terms in the binomial: \(a = 9x\) and \(b = 7y\).
Apply the formula \((a + b)^2 = a^2 + 2ab + b^2\) to the given expression. Substitute \(a = 9x\) and \(b = 7y\) into the formula.
Calculate each term separately: \(a^2 = (9x)^2\), \(2ab = 2(9x)(7y)\), and \(b^2 = (7y)^2\).
Combine the results from the previous step to write the expanded form of the expression.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Binomial Expansion
Binomial expansion refers to the process of expanding expressions that are raised to a power, particularly those in the form of (a + b)^n. The expansion can be achieved using the Binomial Theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where k ranges from 0 to n. This theorem provides a systematic way to calculate the coefficients of the expanded terms.
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Special Products - Cube Formulas
Squaring a Binomial
Squaring a binomial involves multiplying the binomial by itself. For a binomial (a + b), the square is calculated as (a + b)(a + b), which results in a^2 + 2ab + b^2. This formula is essential for simplifying expressions like (9x + 7y)^2, as it allows for the direct computation of the resulting polynomial.
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Polynomial Terms
Polynomial terms are expressions that consist of variables raised to non-negative integer powers, multiplied by coefficients. In the context of the expression (9x + 7y)^2, the resulting polynomial will contain terms such as x^2, xy, and y^2, each representing different degrees of the variables. Understanding how to combine like terms is crucial for simplifying the final expression.
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Related Practice
Textbook Question
In Exercises 65–92, factor completely, or state that the polynomial is prime. 6x2−6x−12
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Textbook Question
Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree.
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Textbook Question
Simplify the radical expressions in Exercises 67–74, if possible. ⁵√64x6/⁵√2x
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Textbook Question
Find each product :
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Textbook Question
In Exercises 69–82, simplify each complex rational expression. (1/x + 1/y)/(x+y)
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