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

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Answer 1 · 2016-03-29T19:05:35

#y=x^3-3x^2-9x+27#

Breaking it down into parts.

#color(brown)("Step 1"->)# consider #(x-3)^2#

This is #color(magenta)((x-3))color(blue)((x-3))#

This gives;#color(magenta)(" "xcolor(blue)((x-3)) -3color(blue)((x-3))#

#x^2-3x-3x+9" "=" "x^2-6x+9#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Step 2"->)# Now we have #color(magenta)((x+3))color(blue)((x^2-6x+9))#

This is #color(blue)(x^2color(magenta)((x+3))-6xcolor(magenta)((x+3))+9color(magenta)((x+3)))#

#x^3+3x^2-6x^2-18x+9x+27#

#y=x^3-3x^2-9x+27#

Tony B