How do you simplify #3x^2/4 (xy-z) + 4xy/3 (x^2 + 2) - 2x^2/3 (xy-z) + 3xy/5 (x^2 + 2)#?

1 Answer
Oct 22, 2017

Answer:

#(1/60) (507x^3y - 55x^2z + 904xy)#

Explanation:

Let’s first simplify the individual terms and then combine them finally.

#13(x^2/4)(xy - z) = ((13x^2)/4)(xy - z) = (13x^3y)/4 - (13x^2z) / 4 #

#(4x)(y/3)(x^2 + 2) = ((13xy)/3)(x^2 + 2) = (13x^3y)/3 +( 26xy)/3#

#2(x^2/3)(xy-z) = (7x^2/3)(xy - z) = (7x^3y)/3 - (7x^2z )/3#

#(3x)(y/5) (x^2 +2) = ((16xy)/5)(x^2 + 2) =( 16x^3y)/5 + (32xy)/5#

Combining all the terms,

#(13x^3y)/4 -(13x^2z)/4 + (13x^3y)/3 + (26xy)/3 - (7x^3y)/3 + (7x^2z)/3 + (16x^3y)/5+ (32xy)/5#

#=- (13x^2z)/4 + (7x^2z)/3 +(13x^3y)/4 + (13x^3y)/3 - (7x^3y)/3 + (16x^3y)/5 + (26xy)/3 + (32xy)/5#

# = -(11x^2z)/12 + (507x^3y)/60 + (226xy)/15#

#(1/60) (507x^3y - 55x^2z + 904xy)#