Learn Before
Multiplying Using the Distributive Property
Multiply , where the monomial factor contains both a numerical coefficient and a variable.
Step 1 — Distribute: Multiply by each term inside the parentheses:
Step 2 — Simplify: For the first product, multiply the coefficients and apply the Product Property for Exponents , giving . For the second product, :
The result is . When the monomial being distributed has both a coefficient and a variable, each distributed multiplication combines coefficient arithmetic with the Product Property for Exponents — essentially performing a monomial-times-monomial multiplication at each step.
0
1
Tags
OpenStax
Elementary Algebra @ OpenStax
Ch.6 Polynomials - Elementary Algebra @ OpenStax
Algebra
Math
Prealgebra
Related
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying by Distributing and Combining Like Terms
Simplifying by Distributing and Combining Like Terms
Solving by Distributing and Simplifying
Strategy for Solving Linear Equations
Multiplying a Polynomial by a Monomial
Multiplying Using the Distributive Property
Multiplying Using the Distributive Property
Multiplying Using the Distributive Property
A payroll specialist is calculating a standard 5 percent bonus for two different departments. The total bonus can be represented by the expression 0.05(S + M), where S is the total salary of the Sales department and M is the total salary of the Marketing department. Which mathematical property justifies rewriting this expression as 0.05S + 0.05M?
A contractor is calculating the total area of two rooms that have the same width 'w' but different lengths 'l1' and 'l2'. The total area is w(l1 + l2). The contractor calculates the area of each room separately as wl1 + wl2 and then adds them. The mathematical rule that justifies this is the ________ property.
A payroll administrator is expanding the expression 40(r + 2) to calculate total weekly pay including a 2 dollar hourly raise. Arrange the steps in the correct order to expand this expression using the Distributive Property.
An HR manager is simplifying payroll formulas for different departments. Match each initial cost expression on the left with its equivalent simplified form on the right using the distributive property.
A facilities manager is calculating the total cost of upgrading n standard workstations and 5 conference rooms, where the cost per upgrade is x dollars. The total cost is represented by the expression x(n + 5). True or False: According to the distributive property, this expression is equivalent to xn + 5.
Identifying Budgeting Properties in Procurement
Validating Budgeting Formulas in Logistics
Defining the Distributive Property in Administrative Budgeting
A retail manager is calculating the total revenue from selling 'k' holiday gift baskets. Each basket contains a bottle of sparkling cider (c) and a box of chocolates (h). The total revenue is represented by the expression k(c + h). According to the distributive property, which of the following is equivalent to this expression?
A project coordinator is calculating the total labor cost for two separate teams using the expression (Hours_Team_A + Hours_Team_B) × Hourly_Rate. To allocate expenses to different departments, the coordinator rewrites this as (Hours_Team_A × Hourly_Rate) + (Hours_Team_B × Hourly_Rate). Which mathematical property justifies this expansion?
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying 6\left( rac{5}{6}y + rac{1}{2} ight) Using the Distributive Property
Simplifying 12\left( rac{1}{3}n + rac{3}{4} ight) Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Strategy for Solving Equations with Fraction or Decimal Coefficients
Learn After
A facility manager is calculating the total area of two warehouse sections using the expression 7x(2x + y). To expand this expression using the Distributive Property, which of the following shows the correct setup for the first step?
A warehouse manager is using the expression 7x(2x + y) to calculate the total area of two storage zones. According to the Distributive Property, the final simplified expression is ____.
A facility manager is using the mathematical expression 7x(2x + y) to calculate the total square footage of two adjacent storage zones. Match each part of the expanded expression to its correct role in the distribution process.
A logistics coordinator is using the expression $7x(2x + y) to determine the total shipping volume for two different warehouse zones. According to the mechanics of the Distributive Property, expanding the first term ($7x \cdot 2x) requires both multiplying the numerical coefficients and applying the Product Property for Exponents to the variables.
A logistics coordinator is using the expression $7x(2x + y)$ to determine the total storage capacity for two new warehouse sections. Based on the standard procedure for the Distributive Property, arrange the following steps in the correct order to expand this expression.
Analyzing Warehouse Area Calculations
Expanding Warehouse Capacity Expressions
Expanding Professional Inventory Formulas
A floor plan designer is using the expression $7x(2x + y) to calculate the total area of two divided office suites. When applying the Distributive Property to expand this expression, what is the result of the first multiplication step ($7x \cdot 2x)?
A production supervisor uses the formula $7x(2x + y)$ to calculate the total output of two assembly lines. What is the resulting second term when this expression is expanded?