What is the standard form of # y= (5x-2)^3+(-3x-1)^2#?
1 Answer
Dec 26, 2015
Explanation:
To rewrite the equation in standard form, expand the brackets:
#y=(5x-2)^3+(-3x-1)^2#
#y=(5x-2)(5x-2)(5x-2)+(-3x-1)(-3x-1)#
Expand the first two
#y=(25x^2-20x+4)(5x-2)+(9x^2+6x+1)#
Expand the last
#y=(125x^3-100x^2+20x-50x^2+40x-8)+(9x^2+6x+1)#
Group all like-terms together in the first bracket.
#y=(125x^3-100x^2-50x^2+20x+40x-8)+(9x^2+6x+1)#
Simplify the like-terms in the first bracket.
#y=(125x^3-150x^2+60x-8)+(9x^2+6x+1)#
Group all like-terms together.
#y=125x^3-150x^2+9x^2+60x+6x-8+1#
Simplify.
#y=125x^3-141x^2+66x-7#
