Learn Before
Multiplying Using the FOIL Method
Multiply using the FOIL method — both binomials involve subtraction and contain different variables ( and ), which means the Outer and Inner products may not be like terms.
Step 1 — First: Multiply the first terms: .
Step 2 — Outer: Multiply the outermost terms: .
Step 3 — Inner: Multiply the innermost terms: .
Step 4 — Last: Multiply the last terms: .
Writing all four products in order gives:
Step 5 — Combine like terms: Check each term's variable structure: contains , contains , contains both and , and contains . No two terms share the same variable structure, so there are no like terms to combine.
The result is . This example illustrates that when the two binomials involve different variables, the FOIL product does not simplify to a trinomial. The Outer product () and the Inner product () have different variable parts, so they cannot be combined, leaving the result with four terms.
0
1
Tags
OpenStax
Elementary Algebra @ OpenStax
Ch.6 Polynomials - Elementary Algebra @ OpenStax
Algebra
Math
Prealgebra
Related
Multiplying Using the FOIL Method
Multiplying Using the FOIL Method
Multiplying Using the FOIL Method
Multiplying Using the FOIL Method
Multiplying Using the FOIL Method
Multiplying Using the FOIL Method
Binomial Squares Pattern
Product of Conjugates Pattern
As a project estimator calculating material requirements, you use the FOIL method to expand algebraic expressions. Match each letter of the FOIL mnemonic to the specific pair of terms it directs you to multiply.
A retail manager is using a shortcut to multiply two algebraic expressions representing price and quantity. The FOIL method is a mnemonic that can only be used when both of these expressions are ____.
A production manager uses the FOIL method to calculate the total cost of a manufacturing run where both the quantity and the unit price are expressed as binomials. Arrange the following steps in the correct sequence according to the FOIL mnemonic.
A cost estimator is reviewing a financial model where the total expense is calculated using the FOIL method to multiply two binomial expressions. Which of the following statements correctly describes the mathematical relationship between the FOIL shortcut and standard algebraic multiplication?
Completing the FOIL Procedure
A facility manager is calculating the area of a new storage zone with dimensions represented by the binomials (w + 6) and (h - 2). True or False: In this multi-variable expansion, the manager will need to combine the 'Outer' and 'Inner' products to simplify the final area expression.
Warehouse Space Optimization
Technical Documentation: The FOIL Procedure
A logistics coordinator is expanding a pricing model represented by the expression , where is the base price and is the delivery distance. According to the FOIL mnemonic, which specific multiplication represents the Inner (I) product of this expansion?
A data analyst is using the FOIL method to expand a growth model represented by the expression . According to the FOIL method documentation, because both binomials involve the same single variable (), the final simplified expression will typically be which type of polynomial?
Multiplying Using the FOIL Method
Multiplying Using the FOIL Method
Multiplying Using the FOIL Method
Multiplying Using the FOIL Method
Multiplying Using the FOIL Method
Simplifying and
Learn After
A project manager is reviewing a calculation for the area of a workspace defined by the expression (3x - y)(2x - 5). To verify the work, the manager breaks down the FOIL method steps. Arrange the following terms in the correct sequence as they would be calculated using the FOIL (First, Outer, Inner, Last) acronym.
A floor supervisor is calculating the dimensions of a workspace using the expression (3x - y)(2x - 5). When using the FOIL method, which two terms are multiplied to determine the 'Inner' product?
An operations analyst is expanding the cost-efficiency expression (3x - y)(2x - 5) where x and y represent two different supply variables. Match each step of the FOIL method to its correct resulting product for this specific expression.
A data analyst is expanding the expression (3x - y)(2x - 5) to determine a weighting factor for a resource allocation model. True or False: When expanding this expression using the FOIL method, the 'Outer' and 'Inner' products are like terms and should be combined to simplify the final result.
Identifying the Outer Product in a FOIL Expansion
A production supervisor is using the algebraic expression to model manufacturing output. When expanding this expression using the FOIL method, the 'Last' product is determined by multiplying the second terms of each binomial ( and ). The resulting value for this 'Last' term is ____.
Space Optimization Model Analysis
Standard Procedure for Expanding Resource Models
A construction manager is using the algebraic expression (3x - y)(2x - 5) to model the square footage of two distinct workspace zones. After using the FOIL method to expand and simplify this expression, how many total terms will the final expression contain?
A supply chain manager is expanding the algebraic expression to model resource distribution. After applying the FOIL method, the manager finds that the result contains four terms: . According to the principles of algebraic expansion, why are there no 'like terms' to combine in this specific result?