Question

разложить многочлен на множетели а) 5y^2(y-4)+(4-y)^2

b) 125a^3+150a^2b+90ab^2+27b^3

 

Answer 1

$5 y^{2} (y-4)+(4-y) ^{2} =(4-y)^{2}-5 y^{2} (4-y)=(4-y)((4-y)-5 y^{2})=(4-y)(4-y-5 y^{2})=(y-4)(5 y^{2}+y-4) 5 y^{2}+y-4=0 D= 1+4*5*4=81$$y1= frac{-1-9}{10} =-1 y2= frac{-1+9}{10} = frac{8}{10} =(y-4)(y+1)(y- frac{8}{10} )$

y1=4
y2=-1
y3=8/10