How do you simplify $3 \frac{x^{2}}{4} (x y - z) + 4 x \frac{y}{3} (x^{2} + 2) - 2 \frac{x^{2}}{3} (x y - z) + 3 x \frac{y}{5} (x^{2} + 2)$ $3x^2/4 (xy-z) + 4xy/3 (x^2 + 2) - 2x^2/3 (xy-z) + 3xy/5 (x^2 + 2)$ ?

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How do you simplify $3 \frac{x^{2}}{4} (x y - z) + 4 x \frac{y}{3} (x^{2} + 2) - 2 \frac{x^{2}}{3} (x y - z) + 3 x \frac{y}{5} (x^{2} + 2)$ $3x^2/4 (xy-z) + 4xy/3 (x^2 + 2) - 2x^2/3 (xy-z) + 3xy/5 (x^2 + 2)$ ?

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Answer 1 · 2017-10-22T20:22:58

$(\frac{1}{60}) (507 x^{3} y - 55 x^{2} z + 904 x y)$ $(1/60) (507x^3y - 55x^2z + 904xy)$

Explanation:

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

$13 (\frac{x^{2}}{4}) (x y - z) = (\frac{13 x^{2}}{4}) (x y - z) = \frac{13 x^{3} y}{4} - \frac{13 x^{2} z}{4}$ $13(x^2/4)(xy - z) = ((13x^2)/4)(xy - z) = (13x^3y)/4 - (13x^2z) / 4$

$(4 x) (\frac{y}{3}) (x^{2} + 2) = (\frac{13 x y}{3}) (x^{2} + 2) = \frac{13 x^{3} y}{3} + \frac{26 x y}{3}$ $(4x)(y/3)(x^2 + 2) = ((13xy)/3)(x^2 + 2) = (13x^3y)/3 +( 26xy)/3$

$2 (\frac{x^{2}}{3}) (x y - z) = (7 \frac{x^{2}}{3}) (x y - z) = \frac{7 x^{3} y}{3} - \frac{7 x^{2} z}{3}$ $2(x^2/3)(xy-z) = (7x^2/3)(xy - z) = (7x^3y)/3 - (7x^2z )/3$

$(3 x) (\frac{y}{5}) (x^{2} + 2) = (\frac{16 x y}{5}) (x^{2} + 2) = \frac{16 x^{3} y}{5} + \frac{32 x y}{5}$ $(3x)(y/5) (x^2 +2) = ((16xy)/5)(x^2 + 2) =( 16x^3y)/5 + (32xy)/5$

Combining all the terms,

$\frac{13 x^{3} y}{4} - \frac{13 x^{2} z}{4} + \frac{13 x^{3} y}{3} + \frac{26 x y}{3} - \frac{7 x^{3} y}{3} + \frac{7 x^{2} z}{3} + \frac{16 x^{3} y}{5} + \frac{32 x y}{5}$ $(13x^3y)/4 -(13x^2z)/4 + (13x^3y)/3 + (26xy)/3 - (7x^3y)/3 + (7x^2z)/3 + (16x^3y)/5+ (32xy)/5$

$= - \frac{13 x^{2} z}{4} + \frac{7 x^{2} z}{3} + \frac{13 x^{3} y}{4} + \frac{13 x^{3} y}{3} - \frac{7 x^{3} y}{3} + \frac{16 x^{3} y}{5} + \frac{26 x y}{3} + \frac{32 x y}{5}$ $=- (13x^2z)/4 + (7x^2z)/3 +(13x^3y)/4 + (13x^3y)/3 - (7x^3y)/3 + (16x^3y)/5 + (26xy)/3 + (32xy)/5$

$= - \frac{11 x^{2} z}{12} + \frac{507 x^{3} y}{60} + \frac{226 x y}{15}$ $= -(11x^2z)/12 + (507x^3y)/60 + (226xy)/15$

$(\frac{1}{60}) (507 x^{3} y - 55 x^{2} z + 904 x y)$ $(1/60) (507x^3y - 55x^2z + 904xy)$

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How do you simplify $3 \frac{x^{2}}{4} (x y - z) + 4 x \frac{y}{3} (x^{2} + 2) - 2 \frac{x^{2}}{3} (x y - z) + 3 x \frac{y}{5} (x^{2} + 2)$ $3x^2/4 (xy-z) + 4xy/3 (x^2 + 2) - 2x^2/3 (xy-z) + 3xy/5 (x^2 + 2)$ ?

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Explanation:

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How do you simplify $3 \frac{x^{2}}{4} (x y - z) + 4 x \frac{y}{3} (x^{2} + 2) - 2 \frac{x^{2}}{3} (x y - z) + 3 x \frac{y}{5} (x^{2} + 2)$ $3x^2/4 (xy-z) + 4xy/3 (x^2 + 2) - 2x^2/3 (xy-z) + 3xy/5 (x^2 + 2)$ ?