Question

How do the letters in "FOIL" help you remember how to multiply two binomials?

Short answer

The letters in 'FOIL' stand for First, Outer, Inner, and Last. These phrases correspond to the order in which terms of two binomials should be multiplied: First terms of both, the Outer terms in the product, the Inner terms, and finally the Last terms of both binomials. The FOIL method helps in quickly expanding the product of two binomials.

Step-by-step solution

Explanation of FOIL

FOIL is a mnemonic device used to remember the appropriate process for multiplying two binomials. Here, 'F' stands for First, 'O' for Outer, 'I' for Inner and 'L' for Last. This letter acronyms correspond to the terms in the binomial expressions that are being multiplied together.

Apply 'F' in FOIL to binomials

Take any two binomials such as \( (a+b) \) and \( (c+d) \). Applying 'F' (first) means multiplying the first terms of both binomials. In our specific case, the multiplication of the first terms is \( a \cdot c \).

Apply 'O' in FOIL to binomials

Next, applying 'O' (outer) means multiplying the outermost terms of the binomial. In this case, the multiplication of the outer terms is \( a \cdot d \).

Apply 'I' in FOIL to binomials

The next step is to apply 'I' (inner) that refers to the multiplication of the innermost terms of the binomial. Here, that multiplication is \( b \cdot c \).

Apply 'L' in FOIL to binomials

Lastly, applying 'L' (last) means multiplying the last terms of both binomials. Now, that multiplication is \( b \cdot d \). Now, add up all these four results to get the answer.

Final Result

\( (a+b) \cdot (c+d) = a \cdot c + a \cdot d + b \cdot c + b \cdot d \). This is the expansion of the product of two binomials using FOIL.