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In algebra, simplifying expressions is crucial to make them easier to understand and work with. Simplifying involves performing operations to reduce an expression to its simplest form. Here, we'll break down the steps for simplifying an expression.
To start, let's look at the exercise: simplify 9(5u + 8) + 2(u - 6).
First, use the distributive property to eliminate the parentheses. This involves multiplying each term inside the parentheses by the term outside the parentheses.
For 9(5u + 8), we distribute the 9 across both terms inside the parentheses:
\( 9(5u + 8) = (9 \times 5u) + (9 \times 8) = 45u + 72 \)
For 2(u - 6), distribute the 2 across both terms:
\( 2(u - 6) = (2 \times u) + (2 \times -6) = 2u - 12 \)
Now we need to combine these results: 45u + 72 + 2u - 12. When you combine terms step-by-step, it simplifies your work.

Combining like terms is an essential part of simplifying algebraic expressions. Like terms are terms that have the same variables raised to the same power. This means you can add or subtract their coefficients.
Given the expression 45u + 72 + 2u - 12, we have like terms 45u and 2u, and constants 72 and -12. Group these like terms together:
\( 45u + 2u \) and \( 72 - 12 \)
When combining 45u and 2u, add their coefficients:
\( 45u + 2u = 47u \)
Next, combine the constants 72 and -12:
\( 72 - 12 = 60 \)
Finally, the simplified expression becomes:
\( 47u + 60 \)
By combining like terms, we reduce the expression to its most streamlined form, making it easier to work with and understand.

Algebraic operations include addition, subtraction, multiplication, and division of algebraic expressions. Understanding these operations helps in simplifying expressions and solving equations.
In our example, we performed multiplication using the distributive property:
\( 9(5u + 8) = 45u + 72 \)
and
\( 2(u - 6) = 2u - 12 \)
Next, we used addition and subtraction to combine like terms and constants:
\( 45u + 2u = 47u \)
and
\( 72 - 12 = 60 \)
These steps highlight the use of various algebraic operations to simplify an expression. Mastery of these operations is key to progressing in algebra and solving more complex equations. Understanding the fundamental operations provides a strong foundation for mathematical problem-solving.
Always remember to follow the proper order of operations and carefully apply each step.