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

1 Answer
Bill K.
Jun 29, 2015

#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#.

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