Factor a^4-5a^2+4

Math
a4-5a2+4
Rewrite a4 as (a2)2.
(a2)2-5a2+4
Let u=a2. Substitute u for all occurrences of a2.
u2-5u+4
Factor u2-5u+4 using the AC method.
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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 -5.
-4,-1
Write the factored form using these integers.
(u-4)(u-1)
(u-4)(u-1)
Replace all occurrences of u with a2.
(a2-4)(a2-1)
Rewrite 4 as 22.
(a2-22)(a2-1)
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=2.
(a+2)(a-2)(a2-1)
Rewrite 1 as 12.
(a+2)(a-2)(a2-12)
Factor.
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Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=1.
(a+2)(a-2)((a+1)(a-1))
Remove unnecessary parentheses.
(a+2)(a-2)(a+1)(a-1)
(a+2)(a-2)(a+1)(a-1)
Factor a^4-5a^2+4

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