The technique used for multiplying two binomials is called FOIL method.
The letters FOIL stand for:
F - First O - Outer
I - Inner L - Last
|FIRST||Multiply the "First" terms of each of the two binomials|
|OUTER||Multiply the "Outermost" terms of each of the two binomials|
|INNER||Multiply the "Inner" terms (second term of the first binomial and the first term of the second binomial)|
|LAST||Multiply the "Last" terms of each of the two binomials|
`(a+b)(c+d) = ac (First) + ad (Outer) + bc (text(Inner)) + bd (text(Last))`
The above formula for FOIL method is equivalent to a two-step distributive method. If we use distributive property to multiply the above binomials, the formula is:
`(a+b)(c+d)= a(c+d)+b(c+d)`, which equals to
`ac+ad+bc+bd` (FOIL method)
We use FOIL method to find the product:
Combine these numbers to get the result
We use FOIL method to multiply the two binomials.
Next, we add them all.
FOIL method is
`(a+b)(c+d) = ac + ad + bc + bd`
(First) (Outer) (Inner) (Last)
In this example, let us treat `(3x+y)` as the inner term of the second binomial i.e "c" in the above formula.
When we apply FOIL method to `(x-4) ((3x+y)-2)`, we get
`x(3x+y) + (x)(-2) + (-4)(3x+y) + (-4)(-2)`
`= 3x^2 + xy - 2x -12x - 4y + 8 `
`= 3x^2 + xy -14x - 4y + 8`