# Factor y^4+3y^2-4

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
Factor u2+3u-4 using the AC method.
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

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