$$ \left.3 \frac{3}{5} x^{3}-\frac{2}{5} x-5 a b-3 a b\right)\left(3 a b-\frac{2}{3} a b\right) $$ 4. $$ \left(\frac{3}{5} x^{4}-\frac{2}{5} x^{3}-\frac{3}{5} x^{2} 4\right)(3 a y-2 a b-6 a b) $$ 5. $$ \left(\frac{3}{4} a b-\frac{2}{3} a b-\frac{6}{3} a b-\frac{2}{4} a b^{2}\right)\left(\frac{4}{5} a b^{2}-\frac{2}{4} a\right) $$

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UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Simplify:
  $$\left(3\frac{3}{5}\times x^{3}-\frac{2}{5}x-5ab-3ab\right)\left(3ab-\frac{2}{3}ab\right)$$
- step1: Convert the expressions:
  $$\left(\frac{18}{5}x^{3}-\frac{2}{5}x-5ab-3ab\right)\left(3ab-\frac{2}{3}ab\right)$$
- step2: Subtract the terms:
  $$\left(\frac{18}{5}x^{3}-\frac{2}{5}x-8ab\right)\left(3ab-\frac{2}{3}ab\right)$$
- step3: Subtract the terms:
  $$\left(\frac{18}{5}x^{3}-\frac{2}{5}x-8ab\right)\times \frac{7}{3}ab$$
- step4: Multiply the terms:
  $$\frac{7}{3}ab\left(\frac{18}{5}x^{3}-\frac{2}{5}x-8ab\right)$$
- step5: Rewrite the expression:
  $$\frac{7}{3}\left(\frac{18}{5}x^{3}-\frac{2}{5}x-8ab\right)ab$$
- step6: Multiply the expression:
  $$\frac{14}{15}\left(9x^{3}ab-xab-20a^{2}b^{2}\right)$$
- step7: Rearrange the terms:
  $$\frac{42}{5}x^{3}ab-\frac{14}{15}xab-\frac{56}{3}a^{2}b^{2}$$
Expand the expression $$ \left(\frac{3}{5} x^{4}-\frac{2}{5} x^{3}-\frac{3}{5} x^{2} 4\right)(3 a y-2 a b-6 a b) $$
Simplify the expression by following steps:
- step0: Simplify:
  $$\left(\frac{3}{5}x^{4}-\frac{2}{5}x^{3}-\frac{3}{5}x^{2}\times 4\right)\left(3ay-2ab-6ab\right)$$
- step1: Multiply the terms:
  $$\left(\frac{3}{5}x^{4}-\frac{2}{5}x^{3}-\frac{12}{5}x^{2}\right)\left(3ay-2ab-6ab\right)$$
- step2: Subtract the terms:
  $$\left(\frac{3}{5}x^{4}-\frac{2}{5}x^{3}-\frac{12}{5}x^{2}\right)\left(3ay-8ab\right)$$
- step3: Multiply the expression:
  $$5^{-1}\left(9x^{2}ay-24x^{2}ab-6xay+16xab-36ay+96ab\right)x^{2}$$
- step4: Rearrange the terms:
  $$\frac{9}{5}x^{4}ay-\frac{24}{5}x^{4}ab-\frac{6}{5}x^{3}ay+\frac{16}{5}x^{3}ab-\frac{36}{5}ayx^{2}+\frac{96}{5}abx^{2}$$
Expand the expression $$ \left(\frac{3}{4} a b-\frac{2}{3} a b-\frac{6}{3} a b-\frac{2}{4} a b^{2}\right)\left(\frac{4}{5} a b^{2}-\frac{2}{4} a\right) $$
Simplify the expression by following steps:
- step0: Simplify:
  $$\left(\frac{3}{4}ab-\frac{2}{3}ab-\frac{6}{3}ab-\frac{2}{4}ab^{2}\right)\left(\frac{4}{5}ab^{2}-\frac{2}{4}a\right)$$
- step1: Divide the terms:
  $$\left(\frac{3}{4}ab-\frac{2}{3}ab-2ab-\frac{2}{4}ab^{2}\right)\left(\frac{4}{5}ab^{2}-\frac{2}{4}a\right)$$
- step2: Reduce the fraction:
  $$\left(\frac{3}{4}ab-\frac{2}{3}ab-2ab-\frac{1}{2}ab^{2}\right)\left(\frac{4}{5}ab^{2}-\frac{2}{4}a\right)$$
- step3: Subtract the terms:
  $$\left(-\frac{23}{12}ab-\frac{1}{2}ab^{2}\right)\left(\frac{4}{5}ab^{2}-\frac{2}{4}a\right)$$
- step4: Reduce the fraction:
  $$\left(-\frac{23}{12}ab-\frac{1}{2}ab^{2}\right)\left(\frac{4}{5}ab^{2}-\frac{1}{2}a\right)$$
- step5: Multiply the expression:
  $$-120^{-1}\left(184b^{3}-115b+48b^{4}-30b^{2}\right)a^{2}$$
- step6: Rearrange the terms:
  $$-\frac{23}{15}b^{3}a^{2}+\frac{23}{24}ba^{2}-\frac{2}{5}b^{4}a^{2}+\frac{1}{4}b^{2}a^{2}$$
Aquí están los resultados de las expresiones que proporcionaste:

1. Para la expresión $$ \left(3 \frac{3}{5} x^{3}-\frac{2}{5} x-5 a b-3 a b\right)\left(3 a b-\frac{2}{3} a b\right) $$:
   $$
   \frac{42}{5}x^{3}ab - \frac{14}{15}xab - \frac{56}{3}a^{2}b^{2}
   $$

2. Para la expresión $$ \left(\frac{3}{5} x^{4}-\frac{2}{5} x^{3}-\frac{3}{5} x^{2} 4\right)(3 a y-2 a b-6 a b) $$:
   $$
   \frac{9}{5}x^{4}ay - \frac{24}{5}x^{4}ab - \frac{6}{5}x^{3}ay + \frac{16}{5}x^{3}ab - \frac{36}{5}ayx^{2} + \frac{96}{5}abx^{2}
   $$

3. Para la expresión $$ \left(\frac{3}{4} a b-\frac{2}{3} a b-\frac{6}{3} a b-\frac{2}{4} a b^{2}\right)\left(\frac{4}{5} a b^{2}-\frac{2}{4} a\right) $$:
   $$
   -\frac{23}{15}b^{3}a^{2} + \frac{23}{24}ba^{2} - \frac{2}{5}b^{4}a^{2} + \frac{1}{4}b^{2}a^{2}
   $$

Si necesitas más ayuda o aclaraciones sobre estos resultados, no dudes en preguntar.
Aquí están los resultados simplificados de las expresiones: 1. $$ \left(3 \frac{3}{5} x^{3}-\frac{2}{5} x-5 a b-3 a b\right)\left(3 a b-\frac{2}{3} a b\right) = \frac{42}{5}x^{3}ab - \frac{14}{15}xab - \frac{56}{3}a^{2}b^{2} $$ 2. $$ \left(\frac{3}{5} x^{4}-\frac{2}{5} x^{3}-\frac{3}{5} x^{2} 4\right)(3 a y-2 a b-6 a b) = \frac{9}{5}x^{4}ay - \frac{24}{5}x^{4}ab - \frac{6}{5}x^{3}ay + \frac{16}{5}x^{3}ab - \frac{36}{5}ayx^{2} + \frac{96}{5}abx^{2} $$ 3. $$ \left(\frac{3}{4} a b-\frac{2}{3} a b-\frac{6}{3} a b-\frac{2}{4} a b^{2}\right)\left(\frac{4}{5} a b^{2}-\frac{2}{4} a\right) = -\frac{23}{15}b^{3}a^{2} + \frac{23}{24}ba^{2} - \frac{2}{5}b^{4}a^{2} + \frac{1}{4}b^{2}a^{2} $$ Si necesitas más ayuda o aclaraciones, no dudes en preguntar.

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