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Multiplication is a fundamental operation in math. It involves taking one number and adding it to itself a certain number of times.
For example, when you multiply 9 by 2, it means adding 9 twice, which equals 18.
In the context of algebra, this operation can also be applied to expressions. So when you see an expression like 9(2x + 6), multiplication comes into play by requiring the 9 to be multiplied with both terms inside the parentheses. This step is crucial in solving any problem that involves the distributive property or combining like terms.

The distributive property is a key concept in algebra. It allows you to multiply a single term by each term inside a set of parentheses.
The property is expressed mathematically as: \[ a(b + c) = ab + ac \].
In the exercise, you use this property to distribute the 9 across the terms inside the parentheses (2x + 6).
This means you separately multiply 9 by 2x and 9 by 6. Here's how it works in steps:

• Multiply 9 by 2x: 9 * 2x = 18x
• Multiply 9 by 6: 9 * 6 = 54

The result is then written as a new expression: 18x + 54. The distributive property simplifies complex expressions and makes arithmetic straightforward.

Combining like terms is an important part of simplifying algebraic expressions.
Like terms are terms that have the same variable raised to the same power, even if their coefficients are different. In the exercise, however, we don't have like terms to combine after using the distributive property.
The expression we get, 18x + 54, consists of two separate terms: one involving the variable 'x' (18x) and the other being a constant (54).
In situations where you have like terms, you would add their coefficients to simplify the expression. For example, if you had the expression 3x + 5x, you would combine like terms to get 8x.
This concept keeps algebraic expressions tidy and easier to work with.