Get the solution to "How do you simplify 3x24(xy−z)+4xy3(x2+2)−2x23(xy−z)+3xy5(x2+2)?"

Damian Kerr

Answered question

2022-02-03

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) ?

Zayden Sims

Beginner2022-02-04Added 8 answers

Step 1
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}

(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}

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}

(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}

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} z}{3} + \frac{7 x^{2} z}{3} + \frac{16 x^{3} y}{5} + \frac{32 x y}{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}

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