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# algebra

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104
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Find the constant term in the expansion of (10x^3 - 1/(2x))^4.

Dec 28, 2020

#1
+117
+2

I think this is supposed to be :

$$( 10x^3 - 1 / (2x^2) ) ^5$$

The constant term is :

$$- C(5, 3) \cdot (10x^3)^2 \cdot (\frac{1}{2x^2})^3 =$$
$$-10 \cdot (100 x^6) \cdot (\frac{1}{8x^6} ) =$$

$$- [10 \cdot \frac{100}{8}] \cdot (\frac{x^6}{x^6}) =$$

$$- 125$$

P.S. I changed up CPhill's answer a little, so please give me a little credit also!

Dec 28, 2020

#1
+117
+2

I think this is supposed to be :

$$( 10x^3 - 1 / (2x^2) ) ^5$$

The constant term is :

$$- C(5, 3) \cdot (10x^3)^2 \cdot (\frac{1}{2x^2})^3 =$$
$$-10 \cdot (100 x^6) \cdot (\frac{1}{8x^6} ) =$$

$$- [10 \cdot \frac{100}{8}] \cdot (\frac{x^6}{x^6}) =$$

$$- 125$$

P.S. I changed up CPhill's answer a little, so please give me a little credit also!

cryptoaops Dec 28, 2020
#2
+117576
+1

LOL!!!!....I  gave you a  point, cryptoaops   !!!

CPhill  Dec 28, 2020
#3
+117
+1

Thank you!

cryptoaops  Dec 28, 2020