How do you factor completely x^4-81x4−81?
2 Answers
Aug 14, 2016
Aug 14, 2016
Explanation:
This is a
color(blue)"difference of squares"difference of squares and, in general, factorises as follows.
color(red)(|bar(ul(color(white)(a/a)color(black)(a^2-b^2=(a-b)(a+b))color(white)(a/a)|)))........ (A) here
(x^2)^2=x^4" and " (9)^2=81
rArra=x^2" and " b=9 substituting into (A)
rArrx^4-81=(x^2-9)(x^2+9)........ (B) Now, the factor
x^2-9 " is also a "color(blue)"difference of squares"
rArrx^2-9=(x-3)(x+3) substituting into (B) to complete the factorising.
rArrx^4-81=(x-3)(x+3)(x^2+9)