Question

How do you use FOIL to multiply `(x+2)(6x+10)`?

Answer 1

`6x^2+22x+20`

Explanation:

FOIL stands for "First, Outside, Inside, Last".

When multiplying two binomials `(a+b)*(c+d)`, the distributive and commutative laws are what ultimately allow you to say that the answer is the sum of "First times First" `a*c`, "Outside times Outside" `a*d`, "Inside times Inside" `b*c`, and "Last times Last" `b*d`.

Thus,

`(a+b)*(c+d)=ac+ad+bc+bd`.

Again, the reason this is true is the distributive law (used twice) and the commutative law (in the last step), which allows you to write

`(a+b)*(c+d)=(a+b)*c+(a+b)*d`

`=a*c+b*c+a*d+b*d=ac+ad+bc+bd`.

For the given problem, `a=x`, `b=2`, `c=6x`, `d=10`, so

`(x+2)(6x+10)=6x^2+10x+12x+20=6x^2+22x+20`.