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Algebraic expressions are a way to represent mathematical relationships using letters (variables) and numbers (constants). An example of an algebraic expression is \(-2y(y-8)\). Here, \(y\) is the variable, and the expression involves both multiplication and subtraction. Algebraic expressions are highly versatile and can represent a wide range of mathematical situations.
If you have an algebraic expression within parentheses, like \((y-8)\), it indicates that an operation (in this case, subtraction) applies to the entire group of terms inside the parentheses. Distributing a term, like \(-2y\), over the expression within the parentheses is a fundamental skill for simplifying expressions.

In the context of algebraic expressions, multiplication involves multiplying coefficients (numbers in front of variables) and the variables themselves. For the given expression \(-2y(y-8)\), you will use the distributive property to multiply \(-2y\) by each term in the parentheses.

The steps for multiplication in this example are:

• Multiply \(-2y\) by \(y\) to get \(-2y^2\).
• Multiply \(-2y\) by \(-8\) to get \(+16y\).

Using the distributive property ensures that every term inside the parentheses is accounted for, maintaining the integrity of the expression.

Combining like terms is the process of simplifying algebraic expressions by merging terms that have the same variable raised to the same power. For example, terms like \(-2y^2\) and \(+16y\) cannot be combined because they involve \('y'\) raised to different powers.

After distribution in our exercise, the result is \(-2y^2 + 16y\). Since there are no like terms to combine, this is the final simplified form of the expression. Understanding how to identify and combine like terms is crucial for simplifying complex algebraic expressions and solving equations efficiently.