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The distributive property is a key concept in algebra that helps simplify expressions. It states that multiplying a single term by terms within parentheses affects each term inside separately. For example, in the expression \( a(b + c) \), using the distributive property, you would get \( ab + ac \).

In the given exercise, we use the distributive property to simplify \( 8 - 3(x - 4) \).

We distribute the \(-3\) to both terms inside the parentheses: \[ -3(x - 4) = -3x + 12 \].

Now, our expression looks like this: \[ 8 - 3x + 12 \].

Combining like terms is another fundamental concept in algebra. It involves merging terms that contain the same variables raised to the same power. This simplifies the expression further.

From the previous step, we had the expression \( 8 - 3x + 12 \).

Here, \( 8 \) and \( 12 \) are like terms because they are both constants (they don’t have variables). We combine them by adding their coefficients: \[ 8 + 12 = 20 \].

So, the expression simplifies to \( 20 - 3x \). The variable term \( -3x \) remains as it is because there are no other like terms with the variable \( x \) in this expression.

Algebraic expressions are combinations of variables, numbers, and operators (such as addition and multiplication). They can be simplified, factored, or evaluated.

Consider the original expression \( 8 - 3(x - 4) \). This is an algebraic expression because it involves a variable \( x \) and constants \( 8 \) and \( 4 \), along with subtraction and multiplication operations.

By applying algebraic principles such as the distributive property and combining like terms, we simplified this expression to \( 20 - 3x \).

This final form of the expression is easier to interpret and use in further calculations or to solve equations. Algebraic expressions are the building blocks for creating and solving equations in algebra.