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expand ((5x+3)/(2y+z))^2

الحلّ

expand

(\frac{5 x + 3}{2 y + z})^{2}

الحلّ

\frac{25 x ^{2} + 30 x + 9}{4 y ^{2} + 4 yz + z ^{2}}

خطوات الحلّ

(\frac{5 x + 3}{2 y + z})^{2}

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

:فعّل قانون القوى

= \frac{( 5 x + 3 ) ^{2}}{( 2 y + z ) ^{2}}

(2 y + z)^{2} = 4 y^{2} + 4 yz + z^{2}

= \frac{( 5 x + 3 ) ^{2}}{4 y ^{2} + 4 yz + z ^{2}}

(5 x + 3)^{2} = 25 x^{2} + 30 x + 9

= \frac{25 x ^{2} + 30 x + 9}{4 y ^{2} + 4 yz + z ^{2}}

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