What is expand 1/8 y(6-x-3y)^2 ?

The solution to expand 1/8 y(6-x-3y)^2 is (3y^2x)/4-(9y^2)/2+(9y^3)/8-(3yx)/2+(yx^2)/8+(9y)/2

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expand 1/8 y(6-x-3y)^2

expand

\frac{1}{8} y (6 - x - 3 y)^{2}

\frac{3 y ^{2} x}{4} - \frac{9 y ^{2}}{2} + \frac{9 y ^{3}}{8} - \frac{3 y x}{2} + \frac{y x ^{2}}{8} + \frac{9 y}{2}

Solution steps

\frac{1}{8} y (6 - x - 3 y)^{2}

(6 - x - 3 y)^{2} = 6 y x - 36 y + 9 y^{2} - 12 x + x^{2} + 36

= \frac{1}{8} y (9 y^{2} + 6 y x - 36 y + x^{2} + 36 - 12 x)

Multiply fractions:

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

= \frac{1 \cdot y}{8} (9 y^{2} + 6 y x - 36 y + x^{2} + 36 - 12 x)

Multiply:

1 \cdot y = y

= \frac{y}{8} (9 y^{2} + 6 y x - 36 y + x^{2} + 36 - 12 x)

Multiply fractions:

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

= \frac{y ( 6 y x - 36 y + 9 y ^{2} - 12 x + x ^{2} + 36 )}{8}

Expand

y (6 y x - 36 y + 9 y^{2} - 12 x + x^{2} + 36) : 6 y^{2} x - 36 y^{2} + 9 y^{3} - 12 y x + y x^{2} + 36 y

= \frac{6 y ^{2} x - 36 y ^{2} + 9 y ^{3} - 12 y x + y x ^{2} + 36 y}{8}

Apply the fraction rule:

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

\frac{6 y ^{2} x - 36 y ^{2} + 9 y ^{3} - 12 y x + y x ^{2} + 36 y}{8} = \frac{6 y ^{2} x}{8} - \frac{36 y ^{2}}{8} + \frac{9 y ^{3}}{8} - \frac{12 y x}{8} + \frac{y x ^{2}}{8} + \frac{36 y}{8}

= \frac{6 y ^{2} x}{8} - \frac{36 y ^{2}}{8} + \frac{9 y ^{3}}{8} - \frac{12 y x}{8} + \frac{y x ^{2}}{8} + \frac{36 y}{8}

\frac{6 y ^{2} x}{8} = \frac{3 y ^{2} x}{4}

\frac{36 y ^{2}}{8} = \frac{9 y ^{2}}{2}

\frac{12 y x}{8} = \frac{3 y x}{2}

\frac{36 y}{8} = \frac{9 y}{2}

= \frac{3 y ^{2} x}{4} - \frac{9 y ^{2}}{2} + \frac{9 y ^{3}}{8} - \frac{3 y x}{2} + \frac{y x ^{2}}{8} + \frac{9 y}{2}

- \frac{4}{s ( s ^{2} - 6 s )}

2 (11 - 8)

\frac{x + 7}{( x + 6 ) ^{2}}

\frac{1}{4} (\frac{4}{y} + 4 y)

- \frac{16 x}{( x ^{2} + 4 ) ^{2}}

What is expand 1/8 y(6-x-3y)^2 ?
The solution to expand 1/8 y(6-x-3y)^2 is (3y^2x)/4-(9y^2)/2+(9y^3)/8-(3yx)/2+(yx^2)/8+(9y)/2