Answer:
[tex]24p[/tex]
Step-by-step explanation:
There's a very useful pattern in factoring and multiplying binomials called a difference of squares, and it looks like this:
[tex](x+y)(x-y)=x^2-y^2[/tex]
We can use this difference of squares to factor the expression we've been given, setting [tex]x=2p+3[/tex] and [tex]y=2p-3[/tex] to obtain the expression
[tex](2p+3)^2-(2p-3)^2=[(2p+3)+(2p-3)][(2p+3)-(2p-3)][/tex] (1)
tackling each of the multiplicands on the right:
[tex](2p+3)+(2p-3)=2p+2p+3-3=4p[/tex] (Left)
[tex](2p+3)-(2p-3)=2p-2p+3-(-3)=3+3=6[/tex] (Right)
This simplifies the expression on the right of (1) to [tex]4p\cdot6[/tex], or simply [tex]24p[/tex].
