Multiply Binomials: Distributive Property/FOIL Method

​Multiplying Binomials: Distributive Property/FOIL Method

By Ferdad Roidad

Monomials, Binomials, Trinomials

Classifying Algebraic Expressions Based on Number of Terms

• A term can be a number (a constant), a variable, or the product of a number and a variable or set of variables.

• Terms are separated by addition and/or subtraction symbols.

• Examples of a single term include: 0; 5x ; -29x ; -xyz/8 ; k ; 5/4

• A single term is called a monomial

• The sum (or difference) of 2 terms is called a binomial.

• The sum or difference of 3 terms is called a trinomial.

Examples of monomials, binomials, and trinomials

Distributive Property for Multiplying Binomials:
The FOIL Method

FOIL = First, Outer, Inner, Last

• The Distributive Property is used to remove parentheses and involves multiplying outer terms with inner terms.

• When 2 binomials are multiplied, each term from 1 binomial is multiplied by each term from the other binomial.

• The FOIL Method is a special case of applying the Distributive Property to the product of 2 binomials; F = first, O = outer, I = inner, L = last.

• When 2 binomials are multiplied, there are 2 terms multiplied by 2 terms which results in 4 products

Distributive Property for Multiplying Binomials:
The FOIL Method

FOIL: First Terms, Outer Terms, Inner Terms, Last Terms

​FOIL is the Distributive Property applied to find the product of 2 binomials

Example: Products of Inner and Outer Terms Canceling Out

Multiple Choice

$$\left(x+5\right)\left(x-4\right)$$

The product of the first terms is:

• $$x^2$$

• $$2x$$

• $$5x$$

• $$2x^2$$

• $$-4x$$

Multiple Choice

$$\left(x+5\right)\left(x-4\right)$$

The product of the outer terms is:

• $$x^2$$

• $$4x$$

• $$-4x$$

• $$5x$$

• $$-20$$

Multiple Choice

$$\left(x+5\right)\left(x-4\right)$$

The product of the inner terms is:

• $$x^2$$

• $$2x$$

• $$-4x$$

• $$5x$$

• $$-20$$

Multiple Choice

$$\left(x+5\right)\left(x-4\right)$$

The product of the last terms is:

• $$9$$

• $$-9$$

• $$1$$

• $$-20$$

• $$-1$$

Multiple Choice

$$\left(x+5\right)\left(x-4\right)=$$

Hint: Apply the distributive property/FOIL Method, then combine like terms.

• $$x^2+9x-20$$

• $$x^2-9x-20$$

• $$x^2+x-20$$

• $$x^2+x+1$$

Multiple Choice

$$\left(3x+1\right)\left(3x-1\right)$$

The product of the first terms is:

• $$6x$$

• $$9x$$

• $$6x^2$$

• $$9x^2$$

• $$3x^2$$

Multiple Choice

$$\left(3x+1\right)\left(3x-1\right)$$

The product of the outer terms is:

• $$9x^2$$

• $$3x$$

• $$-3x$$

• $$-1$$

• $$0$$

Multiple Choice

$$\left(3x+1\right)\left(3x-1\right)$$

The product of the inner terms is:

• $$9x^2$$

• $$3x$$

• $$-3x$$

• $$-1$$

• $$0$$

Multiple Choice

$$\left(3x+1\right)\left(3x-1\right)$$

The product of the last terms is:

• $$9x^2$$

• $$-3x$$

• $$0$$

• $$1$$

• $$-1$$

Multiple Choice

$$\left(3x+1\right)\left(3x-1\right)=$$

Hint: Apply the distributive property/FOIL Method, then combine like terms.

• $$6x^2-1$$

• $$9x^2-6x-1$$

• $$9x^2+1$$

• $$9x^2-1$$

Multiple Choice

$$\left(x+y\right)\left(x-y\right)=$$

Hint: Apply the distributive property/FOIL Method, then combine like terms.

• $$2x^2-2y^2$$

• $$x^2-2xy-y^2$$

• $$x^2-y^2$$

• $$x^2$$

Multiple Choice

$$\left(2-x\right)\left(1-x\right)=$$

Hint: Apply the distributive property/FOIL Method, then combine like terms.

• $$2-3x-x^2$$

• $$2+3x+x^2$$

• $$2-3x+x^2$$

• $$3+3x+2x^2$$