What is the standard form of # y= (-2x+5)^3-(2x+2)^2#?

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Answer 1 · 2017-11-16T12:19:20

This is a form of:
#y=ax^3+bx^2+cx+d#

#y=(-2x+5)^3-(2x+2)^2#
#=> y=(-2x+5)*(-2x+5)*(-2x+5)-(2x+2)*(2x+2)#
#=> y=(4x^2-20x+25)*(-2x+5)-(4x^2+8x+4)#

#(4x^2-20x+25)*(-2x+5)=-8x^3+20x^2+40x^2-100x-50x+125#
#= -8x^3+60x^2-150x+125#

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#-(4x^2+8x+4)=-4x^2-8x-4#

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#y=(-2x+5)^3-(2x+2)^2=...= -8x^3+60x^2-150x+125-4x^2-8x-4#
#=> y=-8x^3+56x^2-158x+121#

This is a form of:
#y=ax^3+bx^2+cx+d#
for
#a=-8 , b=56 , c=-158 , d=121#