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

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Answer 1 · 2016-01-12T10:53:30

#x^3 - 10x^2 + 21x - 36 #

To obtain standard form require to expand brackets and collect like terms.

# (x - 3 )^3 - (x + 3 )^2 # can be rewritten as follows :

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

expanding # (x - 3 )^2 = (x- 3 )(x - 3 ) = x^2 - 6x + 9 #

now becomes ;

#(x^2 - 6x +9 )(x - 3 ) - (x + 3 )(x + 3 ) #

expanding both pairs of brackets :

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

now rewriting with no brackets :

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

Finally collect like terms and write expression in descending order ie. term with highest power → term with lowest power (usually constant term.

#rArr (x - 3 )^3 - (x + 3 )^2 = x^3 - 10x^2 + 21x - 36 #