Question

Simplify (2p+3)2 - (2p-3)2 (Give proper detailed answer with all steps)

Answer 1

Answer:

$24p$

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:

$(x+y)(x-y)=x^2-y^2$

We can use this difference of squares to factor the expression we've been given, setting $x=2p+3$ and $y=2p-3$ to obtain the expression

$(2p+3)^2-(2p-3)^2=[(2p+3)+(2p-3)][(2p+3)-(2p-3)]$ (1)

tackling each of the multiplicands on the right:

$(2p+3)+(2p-3)=2p+2p+3-3=4p$ (Left)

$(2p+3)-(2p-3)=2p-2p+3-(-3)=3+3=6$ (Right)

This simplifies the expression on the right of (1) to $4p\cdot6$, or simply $24p$.