91Ó°ÊÓ

The distributive property is a fundamental principle in algebra that allows you to multiply a single term by two or more terms inside a set of parentheses. It helps to simplify expressions and solve equations. In this exercise, we use the distributive property to clear the parentheses by distributing -2 to each term inside them.

First, let's look at the term \( -2(8.4z - 3.1) \). We need to distribute -2 to both 8.4z and -3.1. Here's how we do it step by step:

1. Multiply -2 by 8.4z:
\(-2 * 8.4z = -16.8z\)
2. Multiply -2 by -3.1:
\(-2 * -3.1 = 6.2\)

After distributing, we have:

\( -2(8.4z - 3.1) = -16.8z + 6.2 \)
By applying the distributive property, we have successfully eliminated the parentheses, making the expression easier to simplify further.

Combining like terms means to simplify an expression by adding or subtracting terms that have the same variable raised to the same power. It is an essential skill in algebra to make expressions more manageable.

After distributing in the previous step, we have the expression:

\( -16.8z + 6.2 - 5.3z \)

To combine like terms, we need to identify the terms that have the common variable z. In this case:

• \-16.8z\
• \-5.3z\

Combine these terms by adding their coefficients:

\( -16.8 + -5.3 = -22.1 \)
Therefore, the combined like terms give us:

\( -22.1z \)

The 6.2 term does not have a variable, so it remains as it is. Now our expression looks like this:

\( -22.1z + 6.2 \)

Algebraic simplification involves applying various techniques such as distributing, combining like terms, and performing arithmetic operations to make an expression more concise and easier to understand or solve. Our goal is to reduce a complex expression to its simplest form.

Here's the process we've followed for this exercise:

1. **Distribute the -2**:
\( -2(8.4z - 3.1) = -16.8z + 6.2 \)
2. **Combine like terms** with -5.3z:
\(-16.8z + 6.2 - 5.3z\)
3. Add the coefficients of z:
\( -16.8z - 5.3z = -22.1z \)

This gives us the simplified expression:

\( -22.1z + 6.2 \)

Thus, we have applied distributive property and combined like terms to achieve the final expression in its simplest form. Practicing these steps will make algebraic simplification more intuitive and manageable.