6) \( a x+b x+a y+b y \) 7) \( b x+5 b+2 x+10 \) 8) \( 2 a b-10 a+3 b-15 \) 9) \( x^{2}-y^{2}+5 x-5 y \) 10) \( x^{3}+y^{2}+9 x+9 \)

Did you know that polynomials like the ones you've listed date back to ancient civilizations? Back in Babylonian times, mathematicians were exploring quadratic equations, laying the groundwork for more complex algebraic expressions. This early work was pivotal in the evolution of mathematics, leading to the sophisticated methods we use today! In practical terms, understanding polynomials is crucial in fields like engineering, computer science, and economics. They’re used to model everything from projectile motion to financial forecasts. By mastering how to manipulate and evaluate these polynomial expressions, you equip yourself with the tools to solve real-world problems, making your skills highly applicable and valuable!