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The distributive property is a fundamental algebraic principle used to remove parentheses from expressions. It states that for any numbers or variables, the expression \(a(b + c)\) is equivalent to \(ab + ac\). This property allows us to simplify expressions by spreading a factor across terms inside parentheses.

In our exercise, the expression is \(-11c - (4 - 2c)\). Notice the negative sign in front of the parentheses. To apply the distributive property correctly, think of it as multiplying each term inside the parentheses by \(-1\).

Let's break it down:

• Multiply \(4\) by \(-1\) to get \(-4\).
• Multiply \(-2c\) by \(-1\) to get \(+2c\).

When you do this, the expression becomes \(-11c - 4 + 2c\).

This crucial step clears the parentheses, paving the way for the next process of simplification.

Combining like terms is a technique used to simplify expressions. It involves merging terms that have the same variables raised to the same power. This process reduces the expression to its simplest form.

In our simplified expression, \(-11c - 4 + 2c\), we see terms that have the variable \(c\). These are the like terms: \-11c\ and \2c\.

Combining these like terms involves adding or subtracting their coefficients:

• Take the coefficient \-11\ and add it to \2\.
• This results in \-9c\.

After performing this combination, the expression becomes \(-9c - 4\).

Combining like terms is an essential skill for managing algebraic expressions and making them less complex.

Simplifying expressions is the process of rewriting them in their most concise and straightforward form. This final step ensures the expression is as clear and manageable as possible.

In the example, we are left with the expression \(-9c - 4\). There are no more parentheses and all like terms have been combined. This means the expression cannot be simplified further.

Key steps in simplifying an expression include:

• Using the distributive property to remove parentheses.
• Combining like terms to reduce the number of similar variables.
• Re-evaluating to ensure no further simplification is possible.

Simplifying expressions is vital in algebra as it prepares equations for solving and helps in understanding mathematical relationships.