The acronym FOIL is a 4-letter acronym to help you remember the 4 partial product terms of this product. They are
F (first) = x*x
O (outer) = x*1
I (inner) = 2*x
L (last) = 2*1
The sum of these is
x^2 + x + 2x + 2
Collecting terms, we have as our result
x^2 + 3x + 2
_____
This is fully equivalent to applying the distributive property.
(x+2)(x+1)
= x(x+1) + 2(x+1)
= x*x + x*1 + 2*x + 2*1
= x^2 + 3x + 2
F (first) = x*x
O (outer) = x*1
I (inner) = 2*x
L (last) = 2*1
The sum of these is
x^2 + x + 2x + 2
Collecting terms, we have as our result
x^2 + 3x + 2
_____
This is fully equivalent to applying the distributive property.
(x+2)(x+1)
= x(x+1) + 2(x+1)
= x*x + x*1 + 2*x + 2*1
= x^2 + 3x + 2
