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Simplifying Using the Distributive Property
To simplify the expression , apply the Distributive Property by multiplying the outside factor by each term inside the parentheses. First, multiply by to obtain . Then, multiply by to obtain . Combining these products gives the simplified expression . This provides a foundational review of distributing a numerical constant across a binomial, an essential prerequisite for multiplying polynomials.
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Intermediate Algebra @ OpenStax
Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax
Algebra
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Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
Simplifying Using the Distributive Property
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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.
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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
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A facility manager is ordering supplies for two identical maintenance kits. Each kit contains safety vests and $3{}2(x + 3)$. Using the distributive property, which of the following is the simplified form of this expression?
A contractor is supervising 2 separate construction crews. Each crew consists of general laborers and 3 skilled carpenters, meaning the total number of workers can be represented by the expression . True or False: Applying the distributive property to correctly simplify this expression results in workers.
An office manager is organizing 2 sets of safety kits. Each kit contains high-visibility vests and 3 first-aid packs. The total number of items is represented by the expression . To find the total item count, match each component of the distributive property process with its correct mathematical result.
A project coordinator is doubling an order for a worksite. Each set contains solar panels and 3 battery packs, which can be represented by the expression . Arrange the following steps in the correct order to simplify this expression by distributing the multiplier to each term inside the parentheses.
An inventory manager is auditing 2 identical supply closets. Each closet holds boxes of printer paper and 3 toner cartridges. The total number of items is represented by the expression . When applying the distributive property to simplify this expression, you must multiply the outside factor 2 by each term inside the parentheses. The result is boxes of printer paper and ____ toner cartridges.