Question

expand the following (5-4/y)^4 by binomial theorem​

Answer 1

Step-by-step explanation:

We have,

$\tt{ \green{ \bigg( 5 - \dfrac{4}{y} \bigg)^{4} }}$

$\sf{ = \:^{4}C_{0}( 5) ^{4} -\:^{4}C_{1}( 5) ^{3} \cdot\bigg(\dfrac{4}{y} \bigg) + \:^{4}C_{2}( 5) ^{2} \cdot\bigg(\dfrac{4}{y} \bigg) ^{2} - \:^{4}C_{3}( 5)\cdot\bigg(\dfrac{4}{y} \bigg)^{3} +\:^{4}C_{4} \cdot\bigg(\dfrac{4}{y} \bigg) ^{4} }$

$\sf{ = 625 -4(125) \cdot\bigg(\dfrac{4}{y} \bigg) + 6(25) \cdot\bigg(\dfrac{16}{y ^{2} } \bigg) - 4(5)\cdot\bigg(\dfrac{64}{y^{3} } \bigg) +\bigg(\dfrac{256}{y^{4} } \bigg) }$

$\sf{ = 625 -\dfrac{2000}{y} + \dfrac{2400}{y ^{2} } - \dfrac{1280}{y^{3} }+\dfrac{256}{y^{4} } }$