How do you factor #u^4-81#?
1 Answer
Nov 23, 2016
Explanation:
The difference of squares identity can be written:
#a^2-b^2 = (a-b)(a+b)#
We can use this a couple of times to derive the factors with Real coefficients, as follows:
#u^4-81 = (u^2)^2-9^2#
#color(white)(u^4-81) = (u^2-9)(u^2+9)#
#color(white)(u^4-81) = (u^2-3^2)(u^2+9)#
#color(white)(u^4-81) = (u-3)(u+3)(u^2+9)#
The remaining quadratic factor has no simpler linear factors with Real coefficients since