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Subtract. \( \left(14 y^{2}+8 y-5\right)-\left(6 y^{2}-3 y+17\right) \) A. \( 8 y^{2}+5 y+12 \) B. \( 8 y^{2}+11 y-22 \) C. \( 20 y^{2}+5 y+12 \) D. \( 20 y^{2}+11 y-22 \)

Ask by Barrett Gardner. in the United States
Feb 03,2025

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The answer is \( 8 y^{2} + 11 y - 22 \), choice B.

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First, let's distribute the negative sign to the second polynomial and simplify: \[ (14y^2 + 8y - 5) - (6y^2 - 3y + 17) = 14y^2 + 8y - 5 - 6y^2 + 3y - 17 \] Now, combine like terms: \[ (14y^2 - 6y^2) + (8y + 3y) + (-5 - 17) = 8y^2 + 11y - 22 \] The correct answer is: **B.** \(8 y^{2}+11 y-22\) Now, here's a quick tip: Keep an eye out for distributing the negative sign carefully; it’s a common mistake to forget to flip the signs! If you're interested in polynomials, check out some polynomial long division tutorials! They're a blast and really help in understanding how to handle more complex expressions.

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