expand ((3-5(x+y))^4)/y

الحلّ

expand

\frac{( 3 - 5 ( x + y ) ) ^{4}}{y}

\frac{625 x ^{4}}{y} + 2500 x^{3} - \frac{1500 x ^{3}}{y} + 3750 x^{2} y - 4500 x^{2} + \frac{1350 x ^{2}}{y} + 2500 x y^{2} - 4500 x y + 2700 x - \frac{540 x}{y} + 625 y^{3} - 1500 y^{2} + 1350 y - 540 + \frac{81}{y}

خطوات الحلّ

\frac{( 3 - 5 ( x + y ) ) ^{4}}{y}

(3 - 5 (x + y))^{4} = 625 x^{4} + 2500 x^{3} y - 1500 x^{3} + 3750 x^{2} y^{2} - 4500 x^{2} y + 1350 x^{2} + 2500 x y^{3} - 4500 x y^{2} + 2700 x y - 540 x + 625 y^{4} - 1500 y^{3} + 1350 y^{2} - 540 y + 81

= \frac{625 x ^{4} + 2500 x ^{3} y - 1500 x ^{3} + 3750 x ^{2} y ^{2} - 4500 x ^{2} y + 1350 x ^{2} + 2500 x y ^{3} - 4500 x y ^{2} + 2700 x y - 540 x + 625 y ^{4} - 1500 y ^{3} + 1350 y ^{2} - 540 y + 81}{y}

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

: استخدم ميزات الكسور التالية

\frac{625 x ^{4} + 2500 x ^{3} y - 1500 x ^{3} + 3750 x ^{2} y ^{2} - 4500 x ^{2} y + 1350 x ^{2} + 2500 x y ^{3} - 4500 x y ^{2} + 2700 x y - 540 x + 625 y ^{4} - 1500 y ^{3} + 1350 y ^{2} - 540 y + 81}{y} = \frac{625 x ^{4}}{y} + \frac{2500 x ^{3} y}{y} - \frac{1500 x ^{3}}{y} + \frac{3750 x ^{2} y ^{2}}{y} - \frac{4500 x ^{2} y}{y} + \frac{1350 x ^{2}}{y} + \frac{2500 x y ^{3}}{y} - \frac{4500 x y ^{2}}{y} + \frac{2700 x y}{y} - \frac{540 x}{y} + \frac{625 y ^{4}}{y} - \frac{1500 y ^{3}}{y} + \frac{1350 y ^{2}}{y} - \frac{540 y}{y} + \frac{81}{y}

= \frac{625 x ^{4}}{y} + \frac{2500 x ^{3} y}{y} - \frac{1500 x ^{3}}{y} + \frac{3750 x ^{2} y ^{2}}{y} - \frac{4500 x ^{2} y}{y} + \frac{1350 x ^{2}}{y} + \frac{2500 x y ^{3}}{y} - \frac{4500 x y ^{2}}{y} + \frac{2700 x y}{y} - \frac{540 x}{y} + \frac{625 y ^{4}}{y} - \frac{1500 y ^{3}}{y} + \frac{1350 y ^{2}}{y} - \frac{540 y}{y} + \frac{81}{y}

\frac{2500 x ^{3} y}{y} = 2500 x^{3}

\frac{3750 x ^{2} y ^{2}}{y} = 3750 x^{2} y

\frac{4500 x ^{2} y}{y} = 4500 x^{2}

\frac{2500 x y ^{3}}{y} = 2500 x y^{2}

\frac{4500 x y ^{2}}{y} = 4500 x y

\frac{2700 x y}{y} = 2700 x

\frac{625 y ^{4}}{y} = 625 y^{3}

\frac{1500 y ^{3}}{y} = 1500 y^{2}

\frac{1350 y ^{2}}{y} = 1350 y

\frac{540 y}{y} = 540

= \frac{625 x ^{4}}{y} + 2500 x^{3} - \frac{1500 x ^{3}}{y} + 3750 x^{2} y - 4500 x^{2} + \frac{1350 x ^{2}}{y} + 2500 x y^{2} - 4500 x y + 2700 x - \frac{540 x}{y} + 625 y^{3} - 1500 y^{2} + 1350 y - 540 + \frac{81}{y}

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