What is expand-3/4 (-2/3 z+2)^4 ?

The solution to expand-3/4 (-2/3 z+2)^4 is -(4z^4}{27}+\frac{16z^3)/9-8z^2+16z-12

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expand-3/4 (-2/3 z+2)^4

expand

- \frac{3}{4} (- \frac{2}{3} z + 2)^{4}

- \frac{4 z ^{4}}{27} + \frac{16 z ^{3}}{9} - 8 z^{2} + 16 z - 12

Solution steps

- \frac{3}{4} (- \frac{2}{3} z + 2)^{4}

Expand

(- \frac{2}{3} z + 2)^{4} : \frac{16 z ^{4}}{81} - \frac{64 z ^{3}}{27} + \frac{32 z ^{2}}{3} - \frac{64 z}{3} + 16

= - \frac{3}{4} (\frac{16 z ^{4}}{81} - \frac{64 z ^{3}}{27} + \frac{32 z ^{2}}{3} - \frac{64 z}{3} + 16)

Distribute parentheses

= - \frac{3}{4} \cdot \frac{16 z ^{4}}{81} - \frac{3}{4} (- \frac{64 z ^{3}}{27}) - \frac{3}{4} \cdot \frac{32 z ^{2}}{3} - \frac{3}{4} (- \frac{64 z}{3}) - \frac{3}{4} \cdot 16

Simplify

- \frac{3}{4} \cdot \frac{16 z ^{4}}{81} - \frac{3}{4} (- \frac{64 z ^{3}}{27}) - \frac{3}{4} \cdot \frac{32 z ^{2}}{3} - \frac{3}{4} (- \frac{64 z}{3}) - \frac{3}{4} \cdot 16 : - \frac{4 z ^{4}}{27} + \frac{16 z ^{3}}{9} - 8 z^{2} + 16 z - 12

= - \frac{4 z ^{4}}{27} + \frac{16 z ^{3}}{9} - 8 z^{2} + 16 z - 12

\frac{d}{d x} ((A) (2 x y + \frac{2000}{x} + \frac{2000}{y}))

π (4 - 4 y^{2} + y^{4} - y^{8})

25 (2 + 3)

\frac{64 π ( 2 - 2 )}{3}

What is expand-3/4 (-2/3 z+2)^4 ?
The solution to expand-3/4 (-2/3 z+2)^4 is -(4z^4}{27}+\frac{16z^3)/9-8z^2+16z-12