26) \( 2 x^{3} y+12 x^{2} y+18 x y \) 28) \( 2 x^{2}+8 x+6 \) 30) \( 24 x^{\wedge} 2-52 x y+8 y^{\wedge} 2 \) 32) \( 3 u^{2}+13 u v-10 v^{2} \)
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Beyond the Answer
Did you know that polynomial expressions like those you've mentioned can often be factored to simplify calculations? For example, \( 2x^3y + 12x^2y + 18xy \) can be factored by taking out the greatest common factor, which is \( 2xy \), leaving you with \( 2xy(x^2 + 6x + 9) \). This not only makes the expression easier to handle but reveals more about its structure! When tackling these polynomials, a common mistake is skipping the step of identifying the greatest common factor (GCF) before attempting to factor completely. Always remember to look for a GCF first, as this can drastically simplify the process. For example, in \( 2x^2 + 8x + 6 \), if you factor out a \( 2 \), you're left with \( 2(x^2 + 4x + 3) \), making your life much easier in the long run!
