展开 (3-y-1/2 x)^2-(x/2)^2

解答

展开

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

y x - 3 x + y^{2} - 6 y + 9

求解步骤

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

\frac{1}{2} x = \frac{x}{2}

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

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

将项转换为分式:

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

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

因为分母相等，所以合并分式:

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

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

2^{2} = 4

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

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

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

2^{2} = 4

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

乘开

- x^{2} + (y x - 6 y + y^{2} - 3 x + \frac{x ^{2}}{4} + 9) \cdot 4 : 4 y x - 12 x + 4 y^{2} - 24 y + 36

= \frac{4 y x - 12 x + 4 y ^{2} - 24 y + 36}{4}

分解

4 y x - 12 x + 4 y^{2} - 24 y + 36 : 4 (y x - 3 x + y^{2} - 6 y + 9)

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

数字相除:

\frac{4}{4} = 1

= y x - 3 x + y^{2} - 6 y + 9

s im pl i f y (3 n + 8) (6 n + 12)

\frac{d}{d x} ((z (x, y)) (x + y))

e x p an d \frac{4 x ^{2} + 36 x - 28}{4 x}

e x p an d \frac{2 n ( - 1 ) ^{n + 1} + 3 ( - 1 ) ^{n + 1} - 1}{4}

e x p an d tan^{2} (x) + (3 - 1) tan (x) - 3