The standard form of #y = (2x - 1)^3 - (3x-3)^2#?

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Answer 1 · 2018-01-26T10:20:28

#8x^3-21x^2+24x-10#

First expand #(2x-1)^3#:

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

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

#=8x^3-12x^2+6x-1#

expanding #(3x-3)^2#:

#9x^2-18x+9#

Substituting in the original:

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

#=(8x^3-12x^2+6x-1)-(9x^2-18x+9)#

#=8x^3-12x^2+6x-1 - 9x^2+18x-9#

#=8x^3-21x^2+24x-10#

The standard form of #y = (2x - 1)^3 ­- (3x-3)^2#?