expand ((-4α^2+4αβ)/(β^2))^2

الحلّ

expand

(\frac{- 4 α ^{2} + 4 α β}{β ^{2}})^{2}

\frac{16 α ^{4}}{β ^{4}} - \frac{32 α ^{3}}{β ^{3}} + \frac{16 α ^{2}}{β ^{2}}

خطوات الحلّ

(\frac{- 4 α ^{2} + 4 α β}{β ^{2}})^{2}

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

:فعّل قانون القوى

= \frac{( - 4 α ^{2} + 4 α β ) ^{2}}{( β ^{2} ) ^{2}}

(β^{2})^{2} : β^{4}

= \frac{( - 4 α ^{2} + 4 α β ) ^{2}}{β ^{4}}

(- 4 α^{2} + 4 α β)^{2} = 16 α^{4} - 32 α^{3} β + 16 α^{2} β^{2}

= \frac{16 α ^{4} - 32 α ^{3} β + 16 α ^{2} β ^{2}}{β ^{4}}

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

: استخدم ميزات الكسور التالية

\frac{16 α ^{4} - 32 α ^{3} β + 16 α ^{2} β ^{2}}{β ^{4}} = \frac{16 α ^{4}}{β ^{4}} - \frac{32 α ^{3} β}{β ^{4}} + \frac{16 α ^{2} β ^{2}}{β ^{4}}

= \frac{16 α ^{4}}{β ^{4}} - \frac{32 α ^{3} β}{β ^{4}} + \frac{16 α ^{2} β ^{2}}{β ^{4}}

\frac{32 α ^{3} β}{β ^{4}}

اختزل:

\frac{32 α ^{3}}{β ^{3}}

= \frac{16 α ^{4}}{β ^{4}} - \frac{32 α ^{3}}{β ^{3}} + \frac{16 α ^{2} β ^{2}}{β ^{4}}

\frac{16 α ^{2} β ^{2}}{β ^{4}}

اختزل:

\frac{16 α ^{2}}{β ^{2}}

= \frac{16 α ^{4}}{β ^{4}} - \frac{32 α ^{3}}{β ^{3}} + \frac{16 α ^{2}}{β ^{2}}

e x p an d \frac{x ^{4} - 5 x ^{3} + 1}{( 2 - x ) ( x - 3 )}

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

e x p an d \frac{x ^{3} + ( k - 3 ) x ^{2} + ( k + 4 ) x - 6 k}{( x - 3 )}

e x p an d \frac{1}{( s + 1 ) ^{4}}

e x p an d \frac{1}{2} (arcsin (x) + \frac{π}{2} + \frac{1}{2} sin (2 arcsin (x)))