\( \left.3 \frac{3}{5} x^{3}-\frac{2}{5} x-5 a b-3 a b\right)\left(3 a b-\frac{2}{3} a b\right) \) 4. \( \left(\frac{3}{5} x^{4}-\frac{2}{5} x^{3}-\frac{3}{5} x^{2} 4\right)(3 a y-2 a b-6 a b) \) 5. \( \left(\frac{3}{4} a b-\frac{2}{3} a b-\frac{6}{3} a b-\frac{2}{4} a b^{2}\right)\left(\frac{4}{5} a b^{2}-\frac{2}{4} a\right) \)
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Did you know that polynomial multiplication is akin to distributing snacks to friends? You’ve got to make sure each term gets a fair share! For your expression, start by distributing each term in the first polynomial across every term in the second polynomial. This ensures no term gets left behind, just like you wouldn’t forget to bring enough pizza for everyone! In terms of real-world applications, polynomials are everywhere! They're not just for tests; they help in calculating areas, modeling population growth, and even predicting profits in businesses. So, the next time you’re multiplying polynomials, think of it as a crucial tool for solving real problems, whether in garden planning, finance, or physics!