Factor completely. 44x^(2)-17x^(4)y^(2)z^(4) Answer:

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Factor completely.  44x^(2)-17x^(4)y^(2)z^(4) Answer:

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Identify GCF: Step Title: Identify the Greatest Common Factor (GCF) Concise Step Description: Determine the greatest common factor of the terms in the expression. Step Calculation: The GCF of 44x^(2) and 17x^(4)y^(2)z^(4) is 1. Step Output: GCF: 1Recognize Negative Factor: Step Title: Recognize the Negative Common Factor Concise Step Description: Since the second term has a negative coefficient, we can factor out -1 to simplify the expression. Step Calculation: Factoring out -1 from the second term to make the leading coefficient positive. Step Output: -1(-44x^(2) + 17x^(4)y^(2)z^(4))Factor Expression: Step Title: Factor the Expression Concise Step Description: Factor the expression inside the parentheses by recognizing it as a difference of squares. Step Calculation: The expression -44x^(2) + 17x^(4)y^(2)z^(4) can be written as a difference of squares: (ax)^2 - (byz)^2, where a^2 = 44, b^2 = 17, x^2 = x^(4), y^2 = y^(2), and z^2 = z^(4). Step Output: -1((√44x)^2 - (√17x^(2)yz^(2))^2)Apply Difference of Squares: Step Title: Apply the Difference of Squares Formula Concise Step Description: Use the difference of squares formula, which is a^2 - b^2 = (a - b)(a + b), to factor the expression. Step Calculation: Factoring the expression using the difference of squares formula gives us -1(√44x - √17x^(2)yz^(2))(√44x + √17x^(2)yz^(2)). Step Output: -1(√44x - √17x^(2)yz^(2))(√44x + √17x^(2)yz^(2))Simplify Square Roots: Step Title: Simplify the Square Roots Concise Step Description: Simplify the square roots in the factored expression. Step Calculation: √44 = √(4*11) = 2√11 and √17x^(2) = x√17, so the factored expression becomes -1(2√11x - x√17yz^(2))(2√11x + x√17yz^(2)). Step Output: -1(2√11x - x√17yz^(2))(2√11x + x√17yz^(2))Factor Out Common x Term: Step Title: Factor Out the Common x Term Concise Step Description: Factor out the common x term from the factored expression. Step Calculation: Factoring out x from both terms in each binomial gives us -1x(2√11 - √17yz^(2))x(2√11 + √17yz^(2)). Step Output: -1x(2√11 - √17yz^(2))x(2√11 + √17yz^(2))Combine x Terms: Step Title: Combine the x Terms Concise Step Description: Combine the x terms into x^2. Step Calculation: Combining the x terms gives us -x^2(2√11 - √17yz^(2))(2√11 + √17yz^(2)). Step Output: -x^2(2√11 - √17yz^(2))(2√11 + √17yz^(2))

Factor completely. $\newline$ $44 x^{2}-17 x^{4} y^{2} z^{4}$ $\newline$ Answer:

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Factor completely. $\newline$ $44 x^{2}-17 x^{4} y^{2} z^{4}$ $\newline$ Answer: