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27) \( x^{2}+10 x y+16 y^{2} \)

Ask by Curry Powell. in the United States
Mar 11,2025

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The expression \( x^{2} + 10xy + 16y^{2} \) can be factored as \( (x + 2y)(x + 8y) \).

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Beyond the Answer

Did you know that the expression \( x^{2}+10xy+16y^{2} \) can be categorized as a quadratic in two variables? This means it forms a conic section when graphed in the Cartesian plane. It could represent a parabola, ellipse, or hyperbola depending on the coefficients involved. In this case, it can be simplified or factored depending on its structure! Now, if you’re looking to factor \( x^{2}+10xy+16y^{2} \) directly, you can think of it like a puzzle! You are trying to express it as \( (x + ay)(x + by) \). By finding numbers that multiply to \( 16y^{2} \) and add up to \( 10y \), you discover that it factors beautifully into \( (x + 2y)(x + 8y) \). Happy factoring!

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