Simplifying by Distributing and Combining Like Terms
To simplify the expression , apply the order of operations, which requires multiplication (distribution) to be performed before subtraction.
Step 1 — Distribute: Multiply the factor by each term inside the parentheses. The subtraction sign before the indicates that is being distributed:
Step 2 — Multiply: Evaluate the products: and :
Step 3 — Combine like terms: Group the constant terms together. The constants are and , and their difference is :
The simplified result is . Distributing the negative factor first is critical before combining any constant terms.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.1 Foundations - Intermediate Algebra @ OpenStax
Algebra
Related
A warehouse manager uses the expression 8 - 2(x + 3) to find the number of empty storage slots remaining after a shipment. According to the order of operations, which step must be performed first to simplify this expression?
A warehouse supervisor uses the expression 8 - 2(x + 3) to determine the number of available loading docks. Arrange the steps in the correct order to simplify this expression according to the order of operations.
A retail analyst uses the expression to calculate the remaining inventory units after two bulk shipments are processed. True or False: To simplify this expression correctly according to the order of operations, the subtraction should be performed as the first step.
An office manager uses the expression $8 - 2(x + 3)$ to determine the number of available workspace cubicles after a reorganization. Based on the order of operations, match each step or component of the simplification process with its correct mathematical value.
Identifying the Distribution Factor in Logistics
A logistics coordinator at a distribution center uses the expression $8 - 2(x + 3)-2 by the constant $3. The value that results from this specific multiplication is ____.
Audit of Operational Formulas
Standardizing Calculation Procedures for Resource Allocation
A project manager is using the formula to calculate the total hours remaining for a construction phase. After correctly applying the distributive property to reach the intermediate step , which two terms in this expression are classified as 'like terms' that can be combined in the final step?
A quality control analyst is auditing a calculation that uses the expression . The analyst notices a colleague subtracted from as the first step, resulting in . To explain why this is incorrect, the analyst must identify the specific mathematical property that requires multiplying the by the terms inside the parentheses before performing any subtraction. Which property is this?
Simplifying by Distributing and Combining Like Terms