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The distributive property is a crucial tool in algebra that allows us to multiply a single term by each term within a set of parentheses. This property is helpful to simplify expressions and make them easier to work with.
To apply the distributive property, you take the term outside the parentheses and multiply it by each term inside.
For instance, in the expression

• \(5(x-1)\),

we multiply 5 by each term inside the parentheses:

• Multiply 5 by \(x\), resulting in \(5x\).
• Multiply 5 by -1, resulting in -5.

After applying the distributive property, the expression \(5(x-1)\) becomes \(5x - 5\). This step makes expressions easier to manage before we move on to other simplification steps, such as combining like terms.

Combining like terms is another essential concept when simplifying algebraic expressions. Once you've applied the distributive property, you should look for terms that can be combined.
'Like terms' are terms within an expression that have the same variable part, although their coefficients might be different.
For instance:

• In the expression \(5x - 5 + 18\), the terms \(-5\) and \(18\) are like terms because they are both constants (they do not include a variable).

To combine them, simply add or subtract their coefficients:

• \(-5 + 18 = 13\).

This step turns our expression into \(5x + 13\), which is much simpler.Remember, combining like terms simplifies expressions and makes them easier to work with.

An algebraic expression is a mathematical phrase that includes numbers, variables, and operations. These expressions don't have an equality sign (unlike equations) and can be found in various forms.
They can be as simple as a single number or variable, or as complex as a lengthy sequence involving multiple terms and operations.
It's important to get familiar with different parts of algebraic expressions:

• Terms: Parts of the expression divided by operators like + or - (e.g., in \(5x - 5 + 18\), there are three terms: \(5x\), -5, and 18).
• Coefficients: The numerical factor of a term with a variable (e.g., 5 is the coefficient of \(x\) in \(5x\)).
• Constants: Numbers without variables (e.g., -5 and 18 are constants).

Understanding algebraic expressions is fundamental to learning algebra, as it sets the stage for solving equations and understanding more complex algebraic concepts. Practice simplifying these expressions by using properties such as the distributive property and combining like terms.