Advertisements
Advertisements
Question
Simplify: \[\frac{3}{2} x^2 ( x^2 - 1) + \frac{1}{4} x^2 ( x^2 + x) - \frac{3}{4}x( x^3 - 1)\]
Solution
To simplify, we will use distributive law as follows:
\[\frac{3}{2} x^2 \left( x^2 - 1 \right) + \frac{1}{4} x^2 \left( x^2 + x \right) - \frac{3}{4}x\left( x^3 - 1 \right)\]
\[ = \frac{3}{2} x^4 - \frac{3}{2} x^2 + \frac{1}{4} x^4 + \frac{1}{4} x^3 - \frac{3}{4} x^4 + \frac{3}{4}x\]
\[ = \frac{3}{2} x^4 + \frac{1}{4} x^4 - \frac{3}{4} x^4 + \frac{1}{4} x^3 - \frac{3}{2} x^2 + \frac{3}{4}x\]
\[ = \left( \frac{6 + 1 - 3}{4} \right) x^4 + \frac{1}{4} x^3 - \frac{3}{2} x^2 + \frac{3}{4}x\]
\[ = x^4 + \frac{1}{4} x^3 - \frac{3}{2} x^2 + \frac{3}{4}x\]
APPEARS IN
RELATED QUESTIONS
Find each of the following product:
\[\left( 0 . 5x \right) \times \left( \frac{1}{3}x y^2 z^4 \right) \times \left( 24 x^2 yz \right)\]
Express each of the following product as a monomials and verify the result in each case for x = 1:
(3x) × (4x) × (−5x)
Simplify: x2(x2 + 1) − x3(x + 1) − x(x3 − x)
Multiply:
(a − 1) by (0.1a2 + 3)
Multiply: \[\left( \frac{3}{5}x + \frac{1}{2}y \right) by \left( \frac{5}{6}x + 4y \right)\]
Multiply:
[−3d + (−7f)] by (5d + f)
Multiply:
(0.8a − 0.5b) by (1.5a − 3b)
Find the following product and verify the result for x = − 1, y = − 2: \[\left( \frac{1}{3}x - \frac{y^2}{5} \right)\left( \frac{1}{3}x + \frac{y^2}{5} \right)\]
Simplify:
x2(x + 2y) (x − 3y)
Simplify : (4m − 8n)2 + (7m + 8n)2
