Multiplying Binomials Using the FOIL Method

Polynomial and Rational Functions

Multiplying Binomials: The FOIL Method

The FOIL method is a systematic technique used to multiply two binomials. FOIL stands for First, Outer, Inner, and Last, referring to the position of each term in the binomials being multiplied.

• First: Multiply the first terms in each binomial.

• Outer: Multiply the outer terms in the product.

• Inner: Multiply the inner terms.

• Last: Multiply the last terms in each binomial.

Given the expression $(x + 1)(x + 6)$, apply the FOIL method as follows:

• First: $x \times x = x^2$

• Outer: $x \times 6 = 6x$

• Inner: $1 \times x = x$

• Last: $1 \times 6 = 6$

Combine all terms:

$x^2 + 6x + x + 6$

Simplify by combining like terms:

$x^2 + 7x + 6$

Example

Multiply $(x + 1)(x + 6)$ using FOIL:

• First: $x^2$

• Outer: $6x$

• Inner: $x$

• Last: $6$

Final Answer: $x^2 + 7x + 6$

Additional info: The FOIL method is a special case of the distributive property for multiplying any two binomials. This technique is foundational for expanding and simplifying polynomial expressions in algebra.