How do you multiply #(2x + 3) (2x - 3)#?

2 Answers
Jul 17, 2015

Answer:

#4x^2-9#

Explanation:

Split one of the brackets:
#(2x+3)(2x-3)=2x(2x-3)+3(2x-3)#

Split the remaining bracket:
#2x(2x)+2x(-3)+3(2x)+3(-3)=4x^2-6x+6x-9#

Combined the expanded terms:
#4x^2-9#

Answer:

Alternatively, use the FOIL mnemonic to pick out pairs of terms to multiply from the two binomials...

Explanation:

#(2x+3)(2x-3)#

#=underbrace(2x*2x)_color(blue)("First")+underbrace(2x*-3)_color(blue)("Outside")+underbrace(3*2x)_color(blue)("Inside")+underbrace(3*-3)_color(blue)("Last")#

#=4x^2-cancel(6x)+cancel(6x)-9#

#=4x^2-9#

Or:
You could use the 'special product' of the form:
#(a+b)(a-b)=a^2-b^2->#
#(2x+3)(2x-3)=(2x)^2-3^2=4x^2-9#