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

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

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

expand

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

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

Solution steps

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

(3 - \frac{3}{2} y - \frac{1}{2} x)^{2} = 9 - 9 y - 3 x + \frac{9 y ^{2} + 6 y x + x ^{2}}{4}

= \frac{1}{2} y (\frac{9 y ^{2} + 6 y x + x ^{2}}{4} + 9 - 9 y - 3 x)

Multiply fractions:

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

= \frac{1 \cdot y}{2} (\frac{9 y ^{2} + 6 y x + x ^{2}}{4} + 9 - 9 y - 3 x)

Multiply:

1 \cdot y = y

= \frac{y}{2} (\frac{9 y ^{2} + 6 y x + x ^{2}}{4} + 9 - 9 y - 3 x)

Multiply fractions:

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

= \frac{y ( 9 - 9 y - 3 x + \frac{9 y ^{2} + 6 y x + x ^{2}}{4} )}{2}

Join

9 - 9 y - 3 x + \frac{9 y ^{2} + 6 y x + x ^{2}}{4} : \frac{36 - 36 y - 12 x + 9 y ^{2} + 6 y x + x ^{2}}{4}

= \frac{\frac{9 y ^{2} + 6 y x - 36 y + x ^{2} + 36 - 12 x}{4} y}{2}

Multiply

y \frac{36 - 36 y - 12 x + 9 y ^{2} + 6 y x + x ^{2}}{4} : \frac{36 y - 36 y ^{2} - 12 y x + 9 y ^{3} + 6 y ^{2} x + y x ^{2}}{4}

= \frac{\frac{36 y - 36 y ^{2} - 12 y x + 9 y ^{3} + 6 y ^{2} x + y x ^{2}}{4}}{2}

Apply the fraction rule:

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

= \frac{36 y - 36 y ^{2} - 12 y x + 9 y ^{3} + 6 y ^{2} x + y x ^{2}}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

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

Apply the fraction rule:

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

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

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

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

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

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

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

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

(1 - i, 2 + 3 i) \cdot (2 + i, 3 - 2 i)

\frac{x + 4}{x ( x + 6 )}

x (x^{4} e^{11 x} + 3)

3 (5 - 2)

(r cos (θ) + r^{2} - 1) (2 r^{2} cos (θ))

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