Problem 46 - Beginning and Intermediate Algebra

Question

Simplify each expression. \(-4 z-8 z\)

Step-by-Step Solution

Answer

-12z

Step 1: Combine Like Terms

Identify the like terms in the expression. In this case, both terms (-4z) and (-8z) are like terms because they have the same variable with the same exponent.

Step 2: Add the Coefficients

Add the coefficients of the like terms. Here you add (-4) and (-8): (-4) + (-8) = (-12).

Step 3: Simplify the Expression

Multiply the combined coefficient by the common variable: (-12z). Therefore, the simplified expression is (-12z).

Key Concepts

simplifying algebraic expressions

Simplifying algebraic expressions helps us to make complex expressions easier to understand and work with.
The process involves combining like terms and performing basic arithmetic operations.
In our example, the expression \(-4z - 8z\) was simplified by combining the like terms and adding their coefficients.

Before you simplify any expression, always:

• Identify all like terms in the expression
• Combine them by adding or subtracting their coefficients

This approach ensures that your final expression is in its simplest form.

adding coefficients

Adding coefficients is a key step in simplifying algebraic expressions.
A coefficient is a numerical value that multiplies a variable in an algebraic term, like \(-4\) in \-4z\.

When you have multiple like terms, you only add their coefficients.

• Identify the coefficients of like terms. In our example, these were \-4\ and \-8\.
• Add them together: \-4 + (-8) = -12\.

Remember, if the coefficients have different signs, perform the addition like normal addition but consider the signs. The general rule is:

• If the coefficients have the same sign, add them and keep the sign.
• If the coefficients have different signs, subtract the smaller one from the larger one and take the sign of the larger one.

This method ensures the correct addition of coefficients.

variable terms

Variable terms are the parts of an algebraic expression that contain variables, like \(-4z\) and \(-8z\) in our example.

Variables represent unknown values and are usually denoted by letters. Variable terms can include coefficients that provide the number by which the variable is multiplied.

When simplifying, always:

• Look for terms with the same variable(s) and exponent(s). These are your like terms.
• Combine them according to their coefficients.

This preserves the integrity of the expression while making it more manageable to work with.