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
