How to factorise #4x^2+4x-1#?
1 Answer
Feb 19, 2018
Explanation:
We can factor this by completing the square then using the difference of squares identity:
#A^2-B^2 = (A-B)(A+B)#
with
#4x^2+4x-1 = 4x^2+4x+1-2#
#color(white)(4x^2+4x-1) = (2x+1)^2-(sqrt(2))^2#
#color(white)(4x^2+4x-1) = ((2x+1)-sqrt(2))((2x+1)+sqrt(2))#
#color(white)(4x^2+4x-1) = (2x+1-sqrt(2))(2x+1+sqrt(2))#