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

1 Answer
Jan 12, 2016

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

Explanation:

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