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Multiplying Using the Distributive Property
Multiply by applying the Distributive Property.
Step 1 — Distribute: Distribute each term of the binomial across the entire trinomial:
Step 2 — Multiply: Expand each product. For the first part: , , and . For the second part: , , and :
Step 3 — Combine like terms: The -terms: . The -terms: :
The result is .
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Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax
Algebra
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A logistics coordinator is simplifying the expression (b + 3)(2b^2 - 5b + 8) to determine shipping volumes. Arrange the following steps in the correct order to solve this using the distributive property as outlined in the course materials.
A small business owner is calculating the total cost of inventory using the expression (b + 3)(2b^2 - 5b + 8). When applying the distributive property to multiply these polynomials, how many individual product terms are generated in the initial expansion before any like terms are combined?
A logistics manager is solving the equation 2x^2 - 3x = 20 to optimize delivery routes. After dividing the entire equation by the leading coefficient to get x^2 - (3/2)x = 10, the manager must add the constant ____ to both sides to complete the square.
A project manager is modeling resource allocation costs using the polynomial expression . Match each mathematical operation from the distributive property expansion with its correct intermediate or simplified result.
A financial analyst is simplifying the expression to model a company's projected revenue growth. True or False: The FOIL (First, Outer, Inner, Last) method can be used as the primary strategy to correctly multiply this binomial by this trinomial.
Mathematical Procedures in Cost Analysis
Standard Procedures for Polynomial Distribution
Fleet Efficiency Modeling Audit
A logistics coordinator is simplifying the expression to model fuel efficiency for a shipping fleet. According to the distributive property procedure, which specific term is produced when the constant '3' from the binomial is multiplied by the middle term '' of the trinomial?
An inventory analyst is using the expression to forecast warehouse space requirements. According to the distributive property procedure, what is the resulting expression after distributing only the variable term from the binomial across the entire trinomial?
Multiplying Using the Distributive Property
Multiplying Using the Distributive Property
Learn After
A manufacturing designer is modeling the displacement of a mechanical component using the algebraic expression . To find the final simplified expression, the designer must correctly apply the distributive property. Arrange the following steps in the correct chronological order as they would appear in the solution process.
A project engineer at a manufacturing plant is using the algebraic expression to model the efficiency rate of a new assembly line over cycles. According to the distributive property, which of the following is the correct first step in setting up the distribution of the binomial terms across the trinomial?
A small business owner uses the algebraic expression to model seasonal sales trends. After applying the distributive property and combining all like terms to simplify the expression, what is the numerical coefficient of the term?
A logistics coordinator is calculating the total volume of storage crates modeled by the expression . To simplify the formula, the coordinator uses the distributive property. Match each specific multiplication operation from the first step of the expansion with its correct resulting term.
A financial analyst relies on the algebraic model to project quarterly revenue. When this expression is fully expanded and the like terms are combined, the resulting simplified formula is .