What is (1/3*a-3/2*b)^3 ?

The solution to (1/3*a-3/2*b)^3 is (a^3}{27}-\frac{a^2b)/2+(9ab^2)/4-(27b^3)/8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (1/3a-3/2b)^3

simplify

(\frac{1}{3} \cdot a - \frac{3}{2} \cdot b)^{3}

\frac{a ^{3}}{27} - \frac{a ^{2} b}{2} + \frac{9 a b ^{2}}{4} - \frac{27 b ^{3}}{8}

Solution steps

(\frac{1}{3} a - \frac{3}{2} b)^{3}

\frac{1}{3} a = \frac{a}{3}

\frac{3}{2} b = \frac{3 b}{2}

= (\frac{a}{3} - \frac{3 b}{2})^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

a = \frac{a}{3}, b = \frac{3 b}{2}

= (\frac{a}{3})^{3} - 3 (\frac{a}{3})^{2} \frac{3 b}{2} + 3 \cdot \frac{a}{3} (\frac{3 b}{2})^{2} - (\frac{3 b}{2})^{3}

Simplify

(\frac{a}{3})^{3} - 3 (\frac{a}{3})^{2} \frac{3 b}{2} + 3 \cdot \frac{a}{3} (\frac{3 b}{2})^{2} - (\frac{3 b}{2})^{3} : \frac{a ^{3}}{27} - \frac{a ^{2} b}{2} + \frac{9 a b ^{2}}{4} - \frac{27 b ^{3}}{8}

= \frac{a ^{3}}{27} - \frac{a ^{2} b}{2} + \frac{9 a b ^{2}}{4} - \frac{27 b ^{3}}{8}

2 (5 x^{2} - 3)^{3}

x^{- 1} 6

3^{x} - 2 + 2

(x + 2)^{2} - 5 x (x + 7) - (x + 1)^{3}

\frac{( 35 b - 42 )}{( 14 b - 7 )}

What is (1/3*a-3/2*b)^3 ?
The solution to (1/3*a-3/2*b)^3 is (a^3}{27}-\frac{a^2b)/2+(9ab^2)/4-(27b^3)/8