Simplifying Algebraic Expressions: 4(2x - 5y) - 5(x + 3y)
In algebra, simplifying expressions is an essential skill to master. It involves combining like terms and eliminating any parentheses or other grouping symbols. In this article, we will explore how to simplify the expression 4(2x - 5y) - 5(x + 3y).
Step 1: Distribute the Numbers
To begin, we need to distribute the numbers outside the parentheses to the terms inside. This means multiplying each term inside the parentheses by the number outside.
4(2x - 5y) = 8x - 20y
-5(x + 3y) = -5x - 15y
Step 2: Combine Like Terms
Now that we have distributed the numbers, we can combine like terms. Like terms are terms that have the same variable and coefficient.
8x - 5x = 3x
-20y - 15y = -35y
Step 3: Write the Simplified Expression
Finally, we can write the simplified expression by combining the like terms.
4(2x - 5y) - 5(x + 3y) = 3x - 35y
And that's it! We have successfully simplified the expression 4(2x - 5y) - 5(x + 3y) to 3x - 35y.
Conclusion
Simplifying algebraic expressions like 4(2x - 5y) - 5(x + 3y) requires attention to detail and a solid understanding of the order of operations. By following the steps outlined above, you can simplify even the most complex expressions. Remember to distribute the numbers, combine like terms, and write the simplified expression. With practice, you'll become a pro at simplifying algebraic expressions!
