Question

Simplify: \[\frac{3}{2} x^2 ( x^2 - 1) + \frac{1}{4} x^2 ( x^2 + x) - \frac{3}{4}x( x^3 - 1)\]

Answer 1

To simplify, we will use distributive law as follows:​

\[\frac{3}{2} x^2 \left( x^2 - 1 \right) + \frac{1}{4} x^2 \left( x^2 + x \right) - \frac{3}{4}x\left( x^3 - 1 \right)\]

\[ = \frac{3}{2} x^4 - \frac{3}{2} x^2 + \frac{1}{4} x^4 + \frac{1}{4} x^3 - \frac{3}{4} x^4 + \frac{3}{4}x\]

\[ = \frac{3}{2} x^4 + \frac{1}{4} x^4 - \frac{3}{4} x^4 + \frac{1}{4} x^3 - \frac{3}{2} x^2 + \frac{3}{4}x\]

\[ = \left( \frac{6 + 1 - 3}{4} \right) x^4 + \frac{1}{4} x^3 - \frac{3}{2} x^2 + \frac{3}{4}x\]

\[ = x^4 + \frac{1}{4} x^3 - \frac{3}{2} x^2 + \frac{3}{4}x\]