Question 9 ( 1 point) Which expression is equivalent to \( 30 x-12 y \) ? \( \begin{array}{ll}\text { a } & 2(15 x+6 y) \\ \text { b } & 6(5 x-12 y) \\ \text { c } & 6(5 x-2 y) \\ \text { d } & x(30-12 y)\end{array} \)

To determine which expression is equivalent to \( 30x - 12y \), let's analyze the options one by one. Starting with option **a**, \( 2(15x + 6y) \): When expanded, this becomes: \[ 2 \cdot 15x + 2 \cdot 6y = 30x + 12y \] This is not equivalent since the sign before \( 12y \) is positive. Next, option **b**, \( 6(5x - 12y) \): When expanded, this gives: \[ 6 \cdot 5x - 6 \cdot 12y = 30x - 72y \] This also is not equivalent. Now looking at option **c**, \( 6(5x - 2y) \): When expanded, you have: \[ 6 \cdot 5x - 6 \cdot 2y = 30x - 12y \] This matches the original expression! Lastly, option **d**, \( x(30 - 12y) \): When expanded, it becomes: \[ 30x - 12xy \] Different enough since it includes \( xy \). So the answer is **c** \( 6(5x - 2y) \). For a bit of fun, let’s review some historical backgrounds of algebra! Algebra, with roots tracing back to ancient Babylonian mathematics, evolved significantly through the work of Persian mathematician Al-Khwarizmi in the 9th century. He’s often referred to as the "father of algebra," and even the term "algebra" derives from his book "Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala," which means "The Compendious Book on Calculation by Completion and Balancing." And if you’re into real-world applications, algebra is everywhere! From calculating expenses and budgeting, to determining the speed of cars in racing video games, understanding how different variables interact helps us make informed decisions. It's not just about x’s and y's; it's about enhancing our everyday lives and problem-solving in the most engaging ways.