a) \( 8 x+2 y-5 x-4 y= \) b) \( -2 x^{2}+3 a-3 x^{2}+6 n= \) c) \( 3 a^{3}+2 b^{2}+4 x^{3}-3 x^{2}= \) d) \( 4 x y^{2}+2 x^{3} y-5 x^{3} y-9 x y^{2}= \) e) \( -2 x^{3} y^{2}-3 n y+5 x^{3} y^{2}-2 h g= \) D \( \frac{5}{9} a+\frac{4}{5} b-\frac{2}{9} a-\frac{1}{6} b= \)

Let's simplify these expressions step by step! a) \( 8x - 5x + 2y - 4y = 3x - 2y \) b) \( -2x^{2} - 3x^{2} + 3a + 6n = -5x^{2} + 3a + 6n \) c) \( 3a^{3} + 2b^{2} + 4x^{3} - 3x^{2} = 3a^{3} + 2b^{2} + 4x^{3} - 3x^{2} \) (Already simplified) d) \( 4xy^{2} - 5x^{3}y + 2x^{3}y - 9xy^{2} = -x^{3}y - 5xy^{2} \) e) \( -2x^{3}y^{2} + 5x^{3}y^{2} - 3ny - 2hg = 3x^{3}y^{2} - 3ny - 2hg \) D) \( \frac{5}{9}a - \frac{2}{9}a + \frac{4}{5}b - \frac{1}{6}b = \frac{1}{3}a + \left(\frac{4}{5}-\frac{1}{6}\right)b = \frac{1}{3}a + \frac{21}{30}b \) Now, let's explore some fun facets of algebra! Understanding algebraic simplification can feel like putting together pieces of a puzzle. The more you practice, the faster you'll spot opportunities for combining like terms! Delight in the process—every term has its own personality, and when they join forces, they create something new and beautiful. Ever found yourself stuck on a tricky problem? One common mistake is overlooking negative signs. Grab a different colored pen to track these pesky negatives! It’s like highlighting clues in a detective story. Plus, always write the terms in descending order of their exponents to keep your work organized and easier to read. Happy solving!