Question

Divide (x^5
-y
^5
) by (x-y) using the method of long division.​

Answer 1

Long Division Method :

$\red{\frac{ (x^{5} - y^{5})}{(x-y)}}$

Q(x)=x⁴+x³y+x²y²+xy³+y⁴

x-y|x⁵-y⁵|

****x⁵-x⁴y

___________

*** x⁴y +0

*** x⁴y-x³y²

___________

***** x³y²+0

***** x³y²-x²y³

____________

******x²y³+0

******x²y³-xy⁴

_____________

****** xy⁴-y⁵

*******xy⁴-y⁵

_____________

********(0)

Dividend = x⁵ - y⁵

Divisor = x-y

Quotient = x⁴+x³y+x²y²+xy³+y⁴

Remainder = 0

Therefore.,

$\red{\frac{(x^{5} - y^{5})}{(x-y)}}$

$\green{ = x^{4}+x^{3}y+x^{2}y^{2}+xy^{3}+y^{4}}$

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