y4+3y2-4

Rewrite y4 as (y2)2.

(y2)2+3y2-4

Let u=y2. Substitute u for all occurrences of y2.

u2+3u-4

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -4 and whose sum is 3.

-1,4

Write the factored form using these integers.

(u-1)(u+4)

(u-1)(u+4)

Replace all occurrences of u with y2.

(y2-1)(y2+4)

Rewrite 1 as 12.

(y2-12)(y2+4)

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=y and b=1.

(y+1)(y-1)(y2+4)

Factor y^4+3y^2-4