I start off with this perfect square and I end up having to use two different trig subs depending on the way the square is made.
Original: $3-2x-x^2$
--Option A--
= $-x^2-2x+3$
= $-(x^2+2x-3)$
= $-(x^2+2x+1-3-1)$
= $-((x+1)^2-4)$
= $-(x+1)^2 + 4$
$4- (x+1)^2$ -> use $a^2-x^2$ trig sub
--Option B--
= $-x^2-2x+3$
$-x^2-2x = -3$
$x^2+2x+1 = 3+1$
$x^2+2x+1 = 4$
$(x+1)^2 = 4$
$(x+1)^2 - 4$ -> use $x^2-a^2$ trig sub
I can understand that both options can be changed by distributing a subtraction sign. Which method is better to create a perfect square in regards to trig sub ? No matter which method I use for trig sub, will I get the same answer ?