Textbook Question
Write each number in scientific notation. −3829
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 81
In Exercises 67–82, find each product. (7xy2−10y)(7xy2+10y)
Verified step by step guidance1
Step 1: Recognize that the given expression is a product of two binomials, (7xy² - 10y) and (7xy² + 10y). This is a special case of the difference of squares formula: (a - b)(a + b) = a² - b².
Step 2: Identify the terms 'a' and 'b' in the binomials. Here, 'a' is 7xy² and 'b' is 10y.
Step 3: Apply the difference of squares formula. Substitute 'a' and 'b' into the formula: a² - b² = (7xy²)² - (10y)².
Step 4: Simplify each squared term. For (7xy²)², square both the coefficient and the variables: (7²)(x²)(y⁴). For (10y)², square the coefficient and the variable: (10²)(y²).
Step 5: Write the simplified expression. Combine the results from Step 4 to express the product as: 49x²y⁴ - 100y².
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Factoring and the Difference of Squares
The expression given is in the form of a difference of squares, which follows the identity a^2 - b^2 = (a - b)(a + b). In this case, 7xy^2 is 'a' and 10y is 'b'. Recognizing this pattern allows for efficient multiplication and simplification of the expression.
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Distributive Property
The distributive property states that a(b + c) = ab + ac. This property is essential for expanding polynomials, as it allows us to multiply each term in one polynomial by each term in the other. Understanding how to apply this property is crucial for correctly finding the product of the two binomials.
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Combining Like Terms
After applying the distributive property, the resulting expression may contain like terms, which are terms that have the same variable factors raised to the same powers. Combining like terms involves adding or subtracting these terms to simplify the expression, leading to a more concise and manageable result.
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Related Practice
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Write each number in scientific notation. 579,000,000,000,000,000
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Perform the indicated operations. Indicate the degree of the resulting polynomial.
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In Exercises 75–82, add or subtract terms whenever possible. ³√54xy3−y³√128x
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