How do you simplify #6x^{\frac{1}{2}}(x^{2}+x)^{2}-8x^{\frac{3}{2}}-8x^{\frac{1}{2}}#?

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Answer 1 · 2017-11-23T12:33:31

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

#f_((x))=6x^(1/2)(x^2+x)^2-8x^(3/2)-8x^(1/2)=#

#=6(x^4+2x^3+x^2)*x^(1/2)-8x*x^(1/2)-8*x^(1/2)=#

#=x^(1/2)[6(x^4+2x^3+x^2)-8x-8]=#

#=[6x^4+12x^3+6x^2-8x-8]sqrtx=#

#=2(sqrtx)(3x^4+6x^3+3x^2-4x-4)=#

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

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

#=2(sqrtx){(x+1)[3x^2(x+1)-4]}=#

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