Question

How do you factor `x^4-82x^2+81`?

Answer 1

`(x-1)(x+1)(x-9)(x+9)`

Explanation:

`x^4 -82x^2+81= x^4 -81x^2-x^2+81`

=`x^2(x^2-81)-(x^2-81)`

=`(x^2-1)(x^2-81)`

=`(x-1)(x+1)(x-9)(x+9)`

Answer 2

Factor the bi-quadratic equation:
y = x^4 - 82x^2 + 81

Ans: (x - 1)(x + 1)(x - 9)(x + 9)

Explanation:

Call x^2 = X
Factor the trinomial: `y = X^2 - 82X + 81`
Find 2 numbers p and q that have same sign.
Factor pairs of (81) --> ( 1, 81). This sum is 82 = -b. The opposite sum gives: p = -1 and q = -81.
`y = (X - 1)(X - 81) = (x^2 - 1)(x^2 - 81)`
`y = (x - 1)(x + 1)(x - 9)(x + 9)`