What is expand (-4(b-1)^3)/(27) ?

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

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expand (-4(b-1)^3)/(27)

expand

\frac{- 4 ( b - 1 ) ^{3}}{27}

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

Solution steps

\frac{- 4 ( b - 1 ) ^{3}}{27}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4 ( b - 1 ) ^{3}}{27}

(b - 1)^{3} = b^{3} - 3 b^{2} + 3 b - 1

= - \frac{4 ( b ^{3} - 3 b ^{2} + 3 b - 1 )}{27}

Expand

4 (b^{3} - 3 b^{2} + 3 b - 1) : 4 b^{3} - 12 b^{2} + 12 b - 4

= - \frac{4 b ^{3} - 12 b ^{2} + 12 b - 4}{27}

Apply the fraction rule:

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

\frac{4 b ^{3} - 12 b ^{2} + 12 b - 4}{27} = - (\frac{4 b ^{3}}{27}) - (- \frac{12 b ^{2}}{27}) - (\frac{12 b}{27}) - (- \frac{4}{27})

= - (\frac{4 b ^{3}}{27}) - (- \frac{12 b ^{2}}{27}) - (\frac{12 b}{27}) - (- \frac{4}{27})

Remove parentheses:

(a) = a, - (- a) = a

= - \frac{4 b ^{3}}{27} + \frac{12 b ^{2}}{27} - \frac{12 b}{27} + \frac{4}{27}

Cancel

\frac{12 b ^{2}}{27} : \frac{4 b ^{2}}{9}

= - \frac{4 b ^{3}}{27} + \frac{4 b ^{2}}{9} - \frac{12 b}{27} + \frac{4}{27}

Cancel

\frac{12 b}{27} : \frac{4 b}{9}

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

\frac{4 ( 2 3 - 9 )}{69}

2 (1 - x - y)^{2}

\frac{d}{d x} ((z) (3 sin (z) x^{2} - 4 x + 2 y z - y^{2}))

(x^{2} - 4) e^{3 x}

3 (1 - e^{- 0.035 t})

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