How do I factor 9-(2x+1)^2

Question

Hi , I need help with factoring  9-(2x+1)^2 

Answer 1

Note that this expression is a difference of perfect squares.  This is because 9 is the square of 3, and (2x + 1) is already squared.  In addition to this, we have a minus sign.  So we can write this as a product of two binomials.

 

(3 + (2x + 1))(3 - (2x + 1))

 

 

Now we can simplify the expression.

 

(4 + 2x)(2 - 2x) =

 

2(2 + x) * 2(1 - x) =

 

4(2 + x)(1 - x)