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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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TOC.tableOfContents
- 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
Capitolo 1, Problema 74
In Exercises 67–82, find each product. (9x+7y)2
Guida verificata passo dopo passo1
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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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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06:24Solving Quadratic Equations by Completing the Square
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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05:13Introduction to Polynomials
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