\( \frac{x}{2} \cdot (2y + 4a + 6c) \) Start with the given expression.
\( \frac{x}{2} \cdot 2 \cdot y + \frac{x}{2} \cdot 4 \cdot a + \frac{x}{2} \cdot 6 \cdot c \) Distribute the \(\frac{x}{2}\) inside the parentheses by multiplying it with each term.
\( \cancel{\frac{x}{2}} \cdot \cancel{2} \cdot y + \frac{x}{2} \cdot 4 \cdot a + \frac{x}{2} \cdot 6 \cdot c \) Prepare to simplify the first term by canceling the 2 in the numerator with the 2 in the denominator.
\( x \cdot y + \cancel{\frac{x}{2}} \cdot \cancel{4} \cdot a + \frac{x}{2} \cdot 6 \cdot c \) Simplify the first term to \(xy\), and prepare to simplify the second term by canceling the 4 with the 2 in the denominator.
\( x \cdot y + 2 \cdot x \cdot a + \cancel{\frac{x}{2}} \cdot \cancel{6} \cdot c \) Simplify the second term to \(2ax\), and prepare to simplify the third term by canceling the 6 with the 2 in the denominator.
\( x \cdot y + 2 \cdot x \cdot a + 3 \cdot x \cdot c \) Simplify the third term to \(3cx\).
\( xy + 2ax + 3cx \) Write the final simplified expression.

Simplifying Complex Mathematical Expressions: A Step-by-Step Guide

Understanding how to simplify complex mathematical expressions is a vital skill in algebra and calculus. In this tutorial, we will take a detailed look at how to simplify the expression \( \frac{x}{3} \cdot (3y – 6a + 9b – 12c) \). Follow along to master the art of simplification!

\( \frac{x}{3} \cdot (3y – 6a + 9b – 12c) \) Start with the given expression.
\( \frac{x}{3} \cdot 3 \cdot y – \frac{x}{3} \cdot 6 \cdot a + \frac{x}{3} \cdot 9 \cdot b – \frac{x}{3} \cdot 12 \cdot c \) Distribute the \(\frac{x}{3}\) inside the parentheses by multiplying it with each term.
\( \cancel{\frac{x}{3}} \cdot \cancel{3} \cdot y – \frac{x}{3} \cdot 6 \cdot a + \frac{x}{3} \cdot 9 \cdot b – \frac{x}{3} \cdot 12 \cdot c \) Prepare to simplify the first term by canceling the 3 in the numerator with the 3 in the denominator.
\( x \cdot y – \cancel{\frac{x}{3}} \cdot \cancel{6} \cdot a + \frac{x}{3} \cdot 9 \cdot b – \frac{x}{3} \cdot 12 \cdot c \) Simplify the first term to \(xy\), and prepare to simplify the second term by canceling the 6 with the 3 in the denominator.
\( x \cdot y – 2 \cdot x \cdot a + \cancel{\frac{x}{3}} \cdot \cancel{9} \cdot b – \frac{x}{3} \cdot 12 \cdot c \) Simplify the second term to \(2ax\), and prepare to simplify the third term by canceling the 9 with the 3 in the denominator.
\( x \cdot y – 2 \cdot x \cdot a + 3 \cdot x \cdot b – \cancel{\frac{x}{3}} \cdot \cancel{12} \cdot c \) Simplify the third term to \(3bx\), and prepare to simplify the fourth term by canceling the 12 with the 3 in the denominator.
\( xy – 2ax + 3bx – 4cx \) Write the final simplified expression.

This step-by-step guide to simplifying a complex mathematical expression provides clear insights into the process of canceling and combining terms. Whether you’re a student, teacher, or math enthusiast, mastering these techniques will enhance your mathematical understanding and problem-solving skills. Explore more tutorials and guides on our website to continue your mathematical journey!

Simplifying Complex Mathematical Expressions: An In-Depth Example

Mastering the art of simplifying complex mathematical expressions is essential in mathematics. In this tutorial, we will explore a new example that illustrates the process of simplifying the expression \( \frac{2x}{4} \cdot (4y – 8z + 12w) \). Follow along to deepen your understanding!

\( \frac{2x}{4} \cdot (4y – 8z + 12w) \) Start with the given expression, focusing on simplifying complex mathematical expressions.
\( \frac{2x}{4} \cdot 4 \cdot y – \frac{2x}{4} \cdot 8 \cdot z + \frac{2x}{4} \cdot 12 \cdot w \) Distribute the \(\frac{2x}{4}\) inside the parentheses by multiplying it with each term.
\( \cancel{\frac{2x}{4}} \cdot \cancel{4} \cdot y – \frac{2x}{4} \cdot 8 \cdot z + \frac{2x}{4} \cdot 12 \cdot w \) Prepare to simplify the first term by canceling the 4 in the numerator with the 4 in the denominator.
\( x \cdot y – \cancel{\frac{2x}{4}} \cdot \cancel{8} \cdot z + \frac{2x}{4} \cdot 12 \cdot w \) Simplify the first term to \(xy\), and prepare to simplify the second term by canceling the 8 with the 4 in the denominator.
\( x \cdot y – 4 \cdot x \cdot z + \cancel{\frac{2x}{4}} \cdot \cancel{12} \cdot w \) Simplify the second term to \(4xz\), and prepare to simplify the third term by canceling the 12 with the 4 in the denominator.
\( xy – 4xz + 6xw \) Write the final simplified expression, completing the process of simplifying complex mathematical expressions.

This tutorial provides a clear and detailed example of simplifying complex mathematical expressions, a fundamental skill in algebra and calculus. By breaking down the process into manageable steps, we make it easy to understand and apply these techniques. Explore more guides and tutorials on our website to continue building your mathematical expertise!