What is expand (3y*(6-y-z)^2)/2 ?

The solution to expand (3y*(6-y-z)^2)/2 is 3y^2z-18y^2+(3y^3)/2-18yz+(3yz^2)/2+54y

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expand (3y*(6-y-z)^2)/2

expand

\frac{3 y \cdot ( 6 - y - z ) ^{2}}{2}

3 y^{2} z - 18 y^{2} + \frac{3 y ^{3}}{2} - 18 yz + \frac{3 y z ^{2}}{2} + 54 y

Solution steps

\frac{3 y ( 6 - y - z ) ^{2}}{2}

(6 - y - z)^{2} = 2 yz - 12 y + y^{2} - 12 z + z^{2} + 36

= \frac{3 y ( y ^{2} + 2 yz - 12 y + z ^{2} + 36 - 12 z )}{2}

Expand

3 y (2 yz - 12 y + y^{2} - 12 z + z^{2} + 36) : 6 y^{2} z - 36 y^{2} + 3 y^{3} - 36 yz + 3 y z^{2} + 108 y

= \frac{6 y ^{2} z - 36 y ^{2} + 3 y ^{3} - 36 yz + 3 y z ^{2} + 108 y}{2}

Apply the fraction rule:

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

\frac{6 y ^{2} z - 36 y ^{2} + 3 y ^{3} - 36 yz + 3 y z ^{2} + 108 y}{2} = \frac{6 y ^{2} z}{2} - \frac{36 y ^{2}}{2} + \frac{3 y ^{3}}{2} - \frac{36 yz}{2} + \frac{3 y z ^{2}}{2} + \frac{108 y}{2}

= \frac{6 y ^{2} z}{2} - \frac{36 y ^{2}}{2} + \frac{3 y ^{3}}{2} - \frac{36 yz}{2} + \frac{3 y z ^{2}}{2} + \frac{108 y}{2}

\frac{6 y ^{2} z}{2} = 3 y^{2} z

\frac{36 y ^{2}}{2} = 18 y^{2}

\frac{36 yz}{2} = 18 yz

\frac{108 y}{2} = 54 y

= 3 y^{2} z - 18 y^{2} + \frac{3 y ^{3}}{2} - 18 yz + \frac{3 y z ^{2}}{2} + 54 y

(- 3, - 1, 1, 2) l e f t (- 1, 0, - 2, - 1)

Δ (3 x - 2)

x (1 + \frac{1}{x})

V (0, 0) F (0, - 6)

\frac{x ( x - 1 ) ( x - 3 ) ( x - 12 ) ( x - 23 ) ( x - 24 )}{40824}

What is expand (3y*(6-y-z)^2)/2 ?
The solution to expand (3y*(6-y-z)^2)/2 is 3y^2z-18y^2+(3y^3)/2-18yz+(3yz^2)/2+54y