\[{x}^{4}-5{x}^{2}+4\]
1
Ask: Which two numbers add up to −5-5 and multiply to 44?
−4-4 and −1-1

2
Rewrite the expression using the above.
(x2−4)(x2−1)({x}^{2}-4)({x}^{2}-1)

3
Rewrite x2−4{x}^{2}-4 in the form a2−b2{a}^{2}-{b}^{2}, where a=xa=x and b=2b=2.
(x2−22)(x2−1)({x}^{2}-{2}^{2})({x}^{2}-1)

4
Use Difference of Squares: a2−b2=(a+b)(a−b){a}^{2}-{b}^{2}=(a+b)(a-b).
(x+2)(x−2)(x2−1)(x+2)(x-2)({x}^{2}-1)

5
Rewrite x2−1{x}^{2}-1 in the form a2−b2{a}^{2}-{b}^{2}, where a=xa=x and b=1b=1.
(x+2)(x−2)(x2−12)(x+2)(x-2)({x}^{2}-{1}^{2})

6
Use Difference of Squares: a2−b2=(a+b)(a−b){a}^{2}-{b}^{2}=(a+b)(a-b).
(x+2)(x−2)(x+1)(x−1)(x+2)(x-2)(x+1)(x-1)

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