What is the FOIL Method for Polynomials?
The FOIL method for polynomials is used in order to multiply quadratics. To see more examples on how to use the FOIL method for polynomials, please view the section below the quiz.
Exercises on Foil Method for Polynomials
Instructions: Use the FOIL method to expand and simplify the algebraic expressions provided below. When you have finished check and compare your work with the solutions given after each question.
| [WpProQuiz 16] |
FOIL Method – Example
You will have several questions on quadratics on the algebra part of your math examination.
Many quadratic expressions are the result of multiplying two binomials.
You will remember that binomials are two terms that are separated by the addition or subtraction sign.
In other words, we can use the FOIL method when polynomials or quadratic equation or expression is in its factored form.
Look at the example below:
(2x + 4)(3x – 1)
This example is a quadratic expression in its factored form.
We perform FOIL by multiplying the terms in this order: First, Outside, Inside, Last.
FIRST:
Let’s look at how to multiply the first terms.
(2x + 4)(3x – 1)
2x and 3x are first in each set of parentheses.
So, we multiply them together.
(2x × 3x) = 2 × 3 × x × x = 6x2
OUTSIDE:
Next we need to multiply the “outside” terms.
(2x + 4)(3x – 1)
2x and –1 are on the outside of the sets of parentheses.
Take care to multiply subtracted numbers as negatives in your multiplication.
So, we multiply the “outside” terms together.
(2x × –1) = 2 × –1 × x = –2x
INSIDE:
The next step is to multiply the “inside” terms.
(2x + 4)(3x – 1)
4 and 3x are on the inside of the sets of parentheses.
So, multiply these terms together.
(4 × 3x) = 4 × 3 × x = 12x
LAST:
The last multiplication operation in the FOIL method is to multiply the last terms.
(2x + 4)(3x – 1)
4 and –1 are the last terms in each set of parentheses.
So, multiply the last terms.
(4 × –1) = –4
THEN SIMPLIFY:
After we have carried out the FOIL method, we need to place all of the above results together in a quadratic expression.
The result of our “First” multiplication was: 6x2
The result of our “Outside” multiplication was: –2x
The result of our “Inside” multiplication was: 12x
The result of our “Last” multiplication was: –4
So, put all of these terms together in a new expression:
6x2 + –2x + 12x + –4
The final step is add like terms together to simplify:
6x2 + –2x + 12x + –4 =
6x2 – 2x + 12x – 4 =
6x2 + 10x – 4
Further Algebra Exercises
You should also look at our posts on quadratics, as well as our other algebra practice problems.
