(2) \( 20-5 y^{2} \) (5) \( 2 x-18 x^{3} \) (8) \( 3 a^{7} b-27 a b^{3} \)
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Beyond the Answer
Did you know that factoring polynomials dates back to ancient civilizations? The Babylonians and Greeks were among the first to understand how to manipulate and simplify these mathematical expressions. By mastering the art of factoring, they not only solved practical problems but also laid down the foundations for modern algebra that we enjoy today! When factoring expressions like \(20 - 5y^2\), it's important to look for common terms. In this case, you can pull out a 5 to simplify it to \(5(4 - y^2)\). For \(2x - 18x^3\), factor out the greatest common factor, which is \(2x\), giving you \(2x(1 - 9x^2)\). Avoid forgetting the negative signs, as they can lead to errors in your factored forms!