Evaluating the product of two binomials using FOIL:
Sum
#color(white)("XXXX")#product of First terms
#color(white)("XXXX")#product of Outside terms
#color(white)("XXXX")#product of Inside terms
#color(white)("XXXX")#product of Last terms
For #(x-8)(x-4)#
#color(white)("XXXX")#First terms: #x, x##color(white)("XXXXXXX")#Product #= x^2#
#color(white)("XXXX")#Outside terms: #x, -4##color(white)("XXX")#Product #= -4x#
#color(white)("XXXX")#Inside terms: #-8, x##color(white)("XXXXX")#Product #= -8xx#
#color(white)("XXXX")#Last terms: #-8, -4##color(white)("XXXXX")#Product #= +32#
Sum
#color(white)("XXXX")##= x^2-4x-8x+32#
Combining terms with same exponent of #x#
#color(white)("XXXX")##= x^2-12x+32#
