What is expand (y(-3y+3)^3)/3 ?

The solution to expand (y(-3y+3)^3)/3 is -9y^4+27y^3-27y^2+9y

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expand (y(-3y+3)^3)/3

expand

\frac{y ( - 3 y + 3 ) ^{3}}{3}

- 9 y^{4} + 27 y^{3} - 27 y^{2} + 9 y

Solution steps

\frac{y ( - 3 y + 3 ) ^{3}}{3}

(- 3 y + 3)^{3} = - 27 y^{3} + 81 y^{2} - 81 y + 27

= \frac{y ( - 27 y ^{3} + 81 y ^{2} - 81 y + 27 )}{3}

Factor

- 27 y^{3} + 81 y^{2} - 81 y + 27 : 27 (- y^{3} + 3 y^{2} - 3 y + 1)

= \frac{y \cdot 27 ( - y ^{3} + 3 y ^{2} - 3 y + 1 )}{3}

Divide the numbers:

\frac{27}{3} = 9

= 9 y (- y^{3} + 3 y^{2} - 3 y + 1)

Distribute parentheses

= 9 y (- y^{3}) + 9 y \cdot 3 y^{2} + 9 y (- 3 y) + 9 y \cdot 1

Apply minus-plus rules

+ (- a) = - a

= - 9 y^{3} y + 9 \cdot 3 y^{2} y - 9 \cdot 3 yy + 9 \cdot 1 \cdot y

Simplify

- 9 y^{3} y + 9 \cdot 3 y^{2} y - 9 \cdot 3 yy + 9 \cdot 1 \cdot y : - 9 y^{4} + 27 y^{3} - 27 y^{2} + 9 y

= - 9 y^{4} + 27 y^{3} - 27 y^{2} + 9 y

\frac{( t ^{2} + 3 ) ^{2}}{t ^{6}}

\frac{1}{x ( 1800 - x )}

sin (x (1 + csc (x)) - sin (x))

(w + x + y + z + 1)^{3}

\frac{x ( x - 5 )}{2}

What is expand (y(-3y+3)^3)/3 ?
The solution to expand (y(-3y+3)^3)/3 is -9y^4+27y^3-27y^2+9y