(2x+1)^2-10(2x+1)+25

Question

From the textbook.

Answer 1

Start by letting y = 2x + 1.  That will make it easier to factor. 

 

So the expression becomes y² - 10y + 25.

 

That's easy to factor as (y - 5)(y - 5) = (y - 5)²

 

Now go back and put 2x - 1 back for y:

 

(y - 5)² = (2x - 1 - 5)² = (2x - 6)² = (2(x - 3))² = 2² (x-3)² = 4 (x-3)²