Method 1: Distribution
#(color(red)(2x+1))(color(green)(x+3))#
#color(white)("XXX")=color(red)(2x)(color(green)(x+3))color(red)(+1)(color(green)(x+3))#
#color(white)("XXX")=(color(teal)(2x*x+2x*3))+(color(brown)(1*x+1*3))#
#color(white)("XXX")=color(teal)(2x^2+6x)+color(brown)(x+3)#
#color(white)("XXX")=color(blue)(2x^2+7x+3)#
Method 2: FOIL
FOIL: First-Outside-Inside-Last is often taught as a method for multiplying two binomials.
Given
#color(white)("XXX")(2x+1)(x+3)#
the First terms are #2x# and #x#
#color(white)("XXX")#Multiplying the First terms gives: #2x^2#
the Outside terms are #2x# and #3#
#color(white)("XXX")#Multiplying the Outside terms gives: #6x#
the Inside terms are #1# and #x#
#color(white)("XXX")#Multiplying the Inside terms gives: #1x#
the Last terms are #1# and #3#
#color(white)("XXX")#Multiplying the Last Terms gives: #3#
Adding the products obtained:
#color(white)("XXX")2x^2+6x+1x+3#
#color(white)("XXXXXXXXX")=2x^2+7x+3#
