91Ó°ÊÓ

The distributive property is a fundamental principle in algebra. It allows you to multiply a number or term by a group of numbers added or subtracted inside parentheses. The formal rule is:
For any number or term a, b, and c:
[ a(b + c) = ab + ac ]
This rule helps in breaking down complex expressions. In our exercise, we use the distributive property to distribute the 6 through the parentheses. So, we multiply 6 by each term inside the parenthesis:
6(3x) = 18x
6(-9) = -54
This simplifies one part of the equation to 18x - 54. Understanding the distributive property is crucial as it is a foundational step in simplifying algebraic expressions.

Combining like terms is the process of simplifying algebraic expressions by adding or subtracting terms with the same variable. Terms are 'like' if they have identical variables raised to the same power. For instance, 3x and -x are like terms because they both have the variable x.
In our exercise, we combine like terms after distributing the minus sign. We have:
18x - 54 - x + 15
Next, group the terms with x: 18x and -x
Combine them: 18x - x = 17x
Then group the constant terms: in -54 and +15
Combine them: -54 + 15 = -39
Now we have the simplified expression 17x - 39. Becoming skilled at identifying and combining like terms simplifies your work greatly.

Simplifying algebraic expressions involves using various algebraic rules to transform a complicated expression into its simplest form. This process often involves:

• Applying the distributive property
• Combining like terms
• Performing arithmetic operations

Each step should be done methodically to ensure no errors are made.
In our exercise, the final step in simplifying the expression is putting it all together. Starting from 6(3x - 9) - (x - 15), we first distributed the terms to get:
18x - 54 - x + 15
Then, combining the like terms:
18x - x = 17x
-54 + 15 = -39
Thus, the final, simplified expression is:
17x - 39
Always recheck each step to make sure all operations are correctly done and the expression is indeed simplified fully. With practice, these steps will become second nature.