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

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)

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