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प्रश्न
Simplify: \[\frac{3}{2} x^2 ( x^2 - 1) + \frac{1}{4} x^2 ( x^2 + x) - \frac{3}{4}x( x^3 - 1)\]
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उत्तर
To simplify, we will use distributive law as follows:
\[\frac{3}{2} x^2 \left( x^2 - 1 \right) + \frac{1}{4} x^2 \left( x^2 + x \right) - \frac{3}{4}x\left( x^3 - 1 \right)\]
\[ = \frac{3}{2} x^4 - \frac{3}{2} x^2 + \frac{1}{4} x^4 + \frac{1}{4} x^3 - \frac{3}{4} x^4 + \frac{3}{4}x\]
\[ = \frac{3}{2} x^4 + \frac{1}{4} x^4 - \frac{3}{4} x^4 + \frac{1}{4} x^3 - \frac{3}{2} x^2 + \frac{3}{4}x\]
\[ = \left( \frac{6 + 1 - 3}{4} \right) x^4 + \frac{1}{4} x^3 - \frac{3}{2} x^2 + \frac{3}{4}x\]
\[ = x^4 + \frac{1}{4} x^3 - \frac{3}{2} x^2 + \frac{3}{4}x\]
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