How do you simplify # [ (x^2-1)^3 (2x+1) ]#?

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Answer 1 · 2018-06-25T10:40:00

#(x^2-1)^3=(x^2-1)(x^2-1)(x^2-1)#

#(x^2-1)(x^2-1)=x^4-2x^2+1#

#(x^4-2x^2+1)(x^2-1)=x^6-2x^4+x^2-x^4+2x^2-1#

#=x^6-3x^4+3x^2-1#

#[(x^2-1)^3(2x+1)]=(x^6-3x^4+3x^2-1)(2x+1)#

=#2x^7-6x^5+6x^3-2x+x^6-3x^4+3x^2-1#

=#2x^7+x^6-6x^5-3x^4+6x^3+3x^2-2x-1#