Question
Simplify: $\frac{3}{2}\text{x}^2\big(\text{x}^2−1\big)+\frac{1}{4}\text{x}^2\big(\text{x}^2+\text{x}\big)−\frac{3}{4}\text{x}\big(\text{x}^3−1\big)$
✓
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}$
$=\frac{3}{2}\text{x}^4+\frac{1}{4}\text{x}^4−\frac{3}{4}\text{x}^4+\frac{1}{4}\text{x}^3−\frac{3}{2}\text{x}^2+\frac{3}{4}\text{x}$
$=\big(\frac{6+1−3}{4}\big)\text{x}^4+\frac{1}{4}\text{x}^3−\frac{3}{2}\text{x}^2+\frac{3}{4}\text{x}$
$=\text{x}^4+\frac{1}{4}\text{x}^3−\frac{3}{2}\text{x}^2+\frac{3}{4}\text{x}$
$=\frac{3}{2}\text{x}^4+\frac{1}{4}\text{x}^4−\frac{3}{4}\text{x}^4+\frac{1}{4}\text{x}^3−\frac{3}{2}\text{x}^2+\frac{3}{4}\text{x}$
$=\big(\frac{6+1−3}{4}\big)\text{x}^4+\frac{1}{4}\text{x}^3−\frac{3}{2}\text{x}^2+\frac{3}{4}\text{x}$
$=\text{x}^4+\frac{1}{4}\text{x}^3−\frac{3}{2}\text{x}^2+\frac{3}{4}\text{x}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
$2$ men or $3$ women can do a piece of work in $16$ days. In how many days can $4$ men and $6$ women do the same work?
→Write the quotient and remainder when we divide:
$\left(2 x^3+x^2-5 x-2\right)$ by $(2 x+3)$
→$\left(2 x^3+x^2-5 x-2\right)$ by $(2 x+3)$
By what number should $\Big(\frac{1}{2}\Big)^{-1}$ be multiplied so that the product may be equal to $\Big(\frac{-4}{7}\Big)^{-1}?$
→Four-fifths of a number is $10$ more than two-thirds of the number. Find the number.
→Solve:
$a^2-2 a b+b^2-c^2$
→$a^2-2 a b+b^2-c^2$
Find the number of sides of a regular polygon when each of its angles has a measures of:- $175^\circ $
→The units digit of a two-digit number is $3$ and seven time the sum of the digits is the number itself. Find the number.
→Mohan wants to buy a trapezium-shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is $10500 m^2$ and the perpendicular distance between the two parallel sides is $100 \ m$, find the length of the side along the river.
→Which of the two rational numbers is greater in the given pair$? \frac{-12}{5}\ \text{or}\ -3$
→A bowler throws a cricket ball at a speed of $120km/h$. How long does this ball take to travel a distance of $20$ metres to reach the batsman?
→