Factor each polynomial. See Examples 5 and 6. (p-2q)2-100

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 66

Chapter 1, Problem 66

Factor each polynomial. See Examples 5 and 6. (p-2q)²-100

Verified step by step guidance

Recognize that the given expression $ (p-2q)^2 - 100 $ is a difference of squares, since it can be written as $ (p-2q)^2 - 10^2 $.

Recall the difference of squares formula: $ a^2 - b^2 = (a - b)(a + b) $. Here, $ a = p - 2q $ and $ b = 10 $.

Apply the formula by substituting $ a $ and $ b $ into it: $ (p - 2q - 10)(p - 2q + 10) $.

Write the factored form clearly as $ (p - 2q - 10)(p - 2q + 10) $.

Verify by expanding the factors to ensure they multiply back to the original expression.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Difference of Squares

The difference of squares is a factoring technique used when an expression is in the form a² - b². It factors into (a - b)(a + b). Recognizing this pattern helps simplify expressions like (p - 2q)² - 100 by identifying a = (p - 2q) and b = 10.

Binomial Squares

A binomial square is an expression of the form (x ± y)², which expands to x² ± 2xy + y². Understanding how to expand and recognize binomial squares is essential for factoring or simplifying expressions involving squared binomials, such as (p - 2q)².

Polynomial Factoring

Polynomial factoring involves rewriting a polynomial as a product of simpler polynomials. Mastery of various factoring methods, including factoring by grouping, special products, and difference of squares, is crucial for breaking down complex expressions into factors.

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