Simplify: 3 2 x^2 (x^2−1 )+1 4 x^2 (x^2+x )−3 4 x (x^3−1 ) - Vidyadip

Question

Simplify:
$\frac{3}{2}\text{x}^2\big(\text{x}^2−1\big)+\frac{1}{4}\text{x}^2\big(\text{x}^2+\text{x}\big)−\frac{3}{4}\text{x}\big(\text{x}^3−1\big)$

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Answer

To simplify, we will use distributive law as follows: $\frac{3}{2}\text{x}^2\big(\text{x}^2−1\big)+\frac{1}{4}\text{x}^2\big(\text{x}^2+\text{x}\big)−\frac{3}{4}\text{x}\big(\text{x}^3−1\big)$$=\frac{3}{2}\text{x}^4−\frac{3}{2}\text{x}^2+\frac{1}{4}\text{x}^4+\frac{1}{4}\text{x}^3−\frac{3}{4}\text{x}^4+\frac{3}{4}\text{x}$
$=\frac{3}{2}\text{x}^4+\frac{1}{4}\text{x}^4−\frac{3}{4}\text{x}^4+\frac{1}{4}\text{x}^3−\frac{3}{2}\text{x}^2+\frac{3}{4}\text{x}$
$=\big(\frac{6+1−3}{4}\big)\text{x}^4+\frac{1}{4}\text{x}^3−\frac{3}{2}\text{x}^2+\frac{3}{4}\text{x}$
$=\text{x}^4+\frac{1}{4}\text{x}^3−\frac{3}{2}\text{x}^2+\frac{3}{4}\text{x}$

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