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2 216. (w+4) ².09 232, (9cf5) (9c-5) 252, (x² + y² > (x²-y5 5 X5

2 216. (w+4) ².09 232, (9cf5) (9c-5) 252, (x² + y² > (x²-y5 5 X5

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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216,232,252
### Polynomial Expressions and Factoring Here are three examples of polynomial expressions: 1. \((w + 4)^2\) This expression represents the square of a binomial. It can be expanded using the formula \((a + b)^2 = a^2 + 2ab + b^2\). 2. \((9c + 5)(9c - 5)\) This is an example of the difference of squares, which follows the formula \((a + b)(a - b) = a^2 - b^2\). Here, it simplifies to \(81c^2 - 25\). 3. \((x^5 + y^5)(x^5 - y^5)\) This expression can be related to the sum and difference of two higher power terms. It follows the identity for the difference of powers: \(a^n - b^n = (a - b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})\). Each expression highlights different algebraic techniques important for simplifying and factoring polynomials.
Transcribed Image Text:### Polynomial Expressions and Factoring Here are three examples of polynomial expressions: 1. \((w + 4)^2\) This expression represents the square of a binomial. It can be expanded using the formula \((a + b)^2 = a^2 + 2ab + b^2\). 2. \((9c + 5)(9c - 5)\) This is an example of the difference of squares, which follows the formula \((a + b)(a - b) = a^2 - b^2\). Here, it simplifies to \(81c^2 - 25\). 3. \((x^5 + y^5)(x^5 - y^5)\) This expression can be related to the sum and difference of two higher power terms. It follows the identity for the difference of powers: \(a^n - b^n = (a - b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})\). Each expression highlights different algebraic techniques important for simplifying and factoring polynomials.
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