Enter the two binomial expressions you wish to expand using the FOIL method. Ensure they are in the format (ax + b)(cx + d), then click 'Calculate. '
Use this online FOIL calculator to multiply two binomials step by step. Learn how the FOIL method works and expand algebraic expressions with ease!
In algebra, the FOIL method is a standard technique that uses the distributive property to multiply two binomials, such as (x + y)(a + b). It breaks down the multiplication into four easy steps:
After performing the multiplication, combine all the resulting terms to simplify the given expression. The FOIL method is a specific application of the distributive law used to multiply two binomials.
In algebra, the distributive property states:
“Multiplying a sum by a number is the same as multiplying each addend separately and then adding the products. For example, x(y + z) = xy + xz”
To know how FOIL relates to distributive property, let's see the multiplication of two binomials (w + x)(y + z):
= (w + x)(y + z)
= w(y + z) + x(y + z) (Distributing (y + z) over (w + x))
= wy + wz + xy + xz (Distributing w and x over (y + z))
As you can see, the FOIL method distributes each term of the first binomial across the second. In the first step, the (y + z) is distributed over the sum in the first expression. In the second step, the distributive law is applied to expand each product resulting from the first step. It shows you are effectively applying the distributive property to simplify the expression.
Multiply the following binomials using the FOIL method:
(2x + 1) (5x + 7)
Solution:
By using the FOIL method:
First (F) = (2x) • (5x) = 10x2
Outer (O) = (2x) • (7) = 14x
Inner (I) = (1) • (5x) = 5x
Last (L) = (1) • (7) = 7
Combine all terms to simplify the algebraic expressions:
= 10x2 + 14x + 5x + 7
= 10x2 + 19x + 7
Multiply the following bionomials:
(4x−5) (x−7)
Solution:
Just follow the letters in FOIL:
First: 4x • x = 4x2
Outer: 4x • (−7) = − 28x
Inner: −5 • x = − 5x
Last: (−5) • (−7) = 35
Sum it all up, and you get: (4x2 − 33x + 35).
For a faster and precise calculation, try our math FOIL calculator.
Fatroing and Foil are two opposite operations. The FOIL method expands two binomials, the factoring process breaks down a polynomial into binomials. Both of these operations undo each other.
For Example:
For reverse operations like factoring, you can use our online factoring calculator.
Follow these steps to use our FOIL method calculator:
You can perform multiple FOIL calculations by clicking the “Re-Calculate” button
Yes, the FOIL method is designed to multiply binomials. For multiplying expressions having more than two terms(like trinomials), the distributive property is used. To practice the distributive property or verify the results of your manual calculations, consider using our distributive property calculator.
The reverse FOIL method, or factoring, is how we factor quadratic trinomials. It is the process of finding the two binomials which, when multiplied, produce the original trinomial.
No, it cannot reverse FOIL operations. This calculator is designed to expand binomials.
References:
From the source of Wikipedia: FOIL Method.
From the source of Chili math: Multiply Binomials Using The FOIL Method.
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