"take out a "color(blue)"common factor "2z^2take out a common factor 2z2
=2z^2(16-t^4)=2z2(16−t4)
16-t^4" is a "color(blue)"difference of squares"16−t4 is a difference of squares
•color(white)(x)a^2-b^2=(a-b)(a+b)∙xa2−b2=(a−b)(a+b)
"here "a=4" and "b=t^2here a=4 and b=t2
16-t^4=(4-t^2)(4+t^2)16−t4=(4−t2)(4+t2)
4-t^2" is also a "color(blue)"difference of squares"4−t2 is also a difference of squares
"here "a=2" and "b=there a=2 and b=t
rArr4-t^2=(2-t)(2+t)⇒4−t2=(2−t)(2+t)
"we can factor "4+t^2" by solving "4+t^2=0we can factor 4+t2 by solving 4+t2=0
4+t^2=0rArrt^2=-4rArrt=+-2i4+t2=0⇒t2=−4⇒t=±2i
rArr4+t^2=(t-2i)(t+2i)⇒4+t2=(t−2i)(t+2i)
rArr32z^2-2t^4z^2=2z^2(2-t)(2+t)(t+2i)(t-2i)⇒32z2−2t4z2=2z2(2−t)(2+t)(t+2i)(t−2i)
