\( 2\left(10-2 x^{2}\right) \) Question 3(Multiple Choice Worth 2 points) (Factoring Algebraic Expressions MC) Rewrite \( \frac{1}{4} x^{3} y+\frac{3}{4} x y^{2} \) using a common factor. \( \frac{1}{4} x y\left(x^{2}+3 y\right) \) \( \frac{1}{4} x^{3} y^{2}(y+3 x) \) \( \frac{1}{2} x y\left(2 x^{2}+6 y\right) \) \( \frac{1}{2} x y\left(x^{2}+3 y\right) \)

Did you know that factoring was a vital skill in ancient mathematics? The Babylonians and Greeks used early forms of algebra to solve equations by breaking them down into simpler components. This method allowed them to tackle complex problems in areas like astronomy, land measurement, and trade. So, next time you factor an expression, remember that this technique has been valued for thousands of years! In the real world, factoring algebraic expressions helps streamline problems in fields like engineering and economics where maximizing or minimizing resources is crucial. For example, when creating a budget or analyzing profit models, breaking down complex equations into their simpler parts makes it easier to identify the most efficient path forward. Understanding how to factor effectively can give you a leg up in various practical scenarios!