Advertisements
Advertisements
Question
Simplify: \[\frac{3}{2} x^2 ( x^2 - 1) + \frac{1}{4} x^2 ( x^2 + x) - \frac{3}{4}x( x^3 - 1)\]
Advertisements
Solution
To simplify, we will use distributive law as follows:
\[\frac{3}{2} x^2 \left( x^2 - 1 \right) + \frac{1}{4} x^2 \left( x^2 + x \right) - \frac{3}{4}x\left( x^3 - 1 \right)\]
\[ = \frac{3}{2} x^4 - \frac{3}{2} x^2 + \frac{1}{4} x^4 + \frac{1}{4} x^3 - \frac{3}{4} x^4 + \frac{3}{4}x\]
\[ = \frac{3}{2} x^4 + \frac{1}{4} x^4 - \frac{3}{4} x^4 + \frac{1}{4} x^3 - \frac{3}{2} x^2 + \frac{3}{4}x\]
\[ = \left( \frac{6 + 1 - 3}{4} \right) x^4 + \frac{1}{4} x^3 - \frac{3}{2} x^2 + \frac{3}{4}x\]
\[ = x^4 + \frac{1}{4} x^3 - \frac{3}{2} x^2 + \frac{3}{4}x\]
RELATED QUESTIONS
Find each of the following product: \[\left( \frac{- 24}{25} x^3 z \right) \times \left( - \frac{15}{16}x z^2 y \right)\]
Find each of the following product: \[\left( \frac{4}{3} u^2 vw \right) \times \left( - 5uv w^2 \right) \times \left( \frac{1}{3} v^2 wu \right)\]
Express each of the following product as a monomials and verify the result in each case for x = 1:
(5x4) × (x2)3 × (2x)2
Express each of the following product as a monomials and verify the result in each case for x = 1:
(x2)3 × (2x) × (−4x) × (5)
Simplify: a(b − c) − b(c − a) − c(a − b)
Simplify: 2a2 + 3a(1 − 2a3) + a(a + 1)
Simplify: a2(2a − 1) + 3a + a3 − 8
Show that: \[\left( \frac{4m}{3} - \frac{3n}{4} \right)^2 + 2mn = \frac{16 m^2}{9} + \frac{9 n^2}{16}\]
Multiply:
23xy2 × 4yz2
What is (−4ab) × (2a²b³)?
