theo bài ra ta có:
\(x^5+y^5=\left(x^4+y^4\right)\left(x+y\right)-xy^4-x^4y\)
\(=\left(\left(x+y\right)-2xy\right)^2-2x^2y^2\)
\(=\left(\left(x+y\right)-2xy\right)\left(\left(x+y\right)-xy\left(x+y\right)^3-3xy\left(x+y\right)\right)\)
\(=\left(a-2b\right)\left(\left(a-ba^3\right)-3ba\right)\)
Có x5 + y5 = ( x3 + y3 )( x2 + y2 ) - x2y2( x + y )
= ( x + y )(x2 - xy + y2 ) ( x+y)2- 2xy -x2y2(x+y)
= a ( x2 -b +y2) (a2 - 2b) - x2y2a
= a [(x +y)2-2xy - b )] .(a2 -2b) - (x.y)2a
= a .[a2 -2b -b] (a2 -2b) -ab2
= a.(a2-3b)(a2-2b)-ab2
=(a3-3ab)(a2-2b)-ab2
= a5 - 2a3b - 3a3b + 6ab2-ab2
= a5 -5a3b+5ab2
