What is expand (((z+12))/2)^3 ?

The solution to expand (((z+12))/2)^3 is (z^3)/8+(9z^2)/2+54z+216

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (((z+12))/2)^3

expand

(\frac{( z + 12 )}{2})^{3}

\frac{z ^{3}}{8} + \frac{9 z ^{2}}{2} + 54 z + 216

Solution steps

(\frac{z + 12}{2})^{3}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( z + 12 ) ^{3}}{2 ^{3}}

(z + 12)^{3} = z^{3} + 36 z^{2} + 432 z + 1728

= \frac{z ^{3} + 36 z ^{2} + 432 z + 1728}{2 ^{3}}

2^{3} = 8

= \frac{z ^{3} + 36 z ^{2} + 432 z + 1728}{8}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{z ^{3} + 36 z ^{2} + 432 z + 1728}{8} = \frac{z ^{3}}{8} + \frac{36 z ^{2}}{8} + \frac{432 z}{8} + \frac{1728}{8}

= \frac{z ^{3}}{8} + \frac{36 z ^{2}}{8} + \frac{432 z}{8} + \frac{1728}{8}

Cancel

\frac{36 z ^{2}}{8} : \frac{9 z ^{2}}{2}

= \frac{z ^{3}}{8} + \frac{9 z ^{2}}{2} + \frac{432 z}{8} + \frac{1728}{8}

Divide the numbers:

\frac{432}{8} = 54

= \frac{z ^{3}}{8} + \frac{9 z ^{2}}{2} + 54 z + \frac{1728}{8}

Divide the numbers:

\frac{1728}{8} = 216

= \frac{z ^{3}}{8} + \frac{9 z ^{2}}{2} + 54 z + 216

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

(4 π + 2) r a d

A (- 3, - 2) B (4, 6)

4 sin (\frac{π}{2} (x - 3)) + 6

15 (\frac{3}{2} + \frac{15}{16} x)^{6}

What is expand (((z+12))/2)^3 ?
The solution to expand (((z+12))/2)^3 is (z^3)/8+(9z^2)/2+54z+216