Question

How do you factor `1-2 sin^2 x + sin^4 x`?

Answer 1

`(1-sin^2x)^2`

Explanation:

`"factor using the a-c method "`

`"let "u=sin^2x`

`rArr1-2u+u^2`

`"the factors of + 1 which sum to - 2 are - 1 and - 1"`

`rArr1-2u+u^2=(1-u)(1-u)=(1-u)^2`

`"change u back to "sin^2x`

`rArr1-2sin^2x+sin^4x`

`=(1-sin^2x)(1-sin^2x)`

`=(1-sin^2x)^2`