Which two numbers add up to -80 and multiply to -81?
-81 and 1
Rewrite the expression using the above
(x^4 - 81)(x^4 + 1)
Rewrite x^4 - 81 in the form; a^2 - b^2, where a = x^2 and b = 9
((x^2)^2 - 9^2)(x^4 + 1)
Use the Difference of Squares: a^2 - b^2 = (a + b)(a - b)
(x^2 + 9)(x^2 - 9)(x^4 + 1)
Rewrite x^2 - 9 in the form a^2 - b^2, where a = x and b = 3
(x^2 + 9)(x^2 - 3^2)(x^4 + 1)
Use the Difference of Squares; a^2 - b^2 = (a + b)(a - b)
(x^2 + 9(x + 3)(x - 3)(x^4 + 1)
