Question

Разложите на неразложимые множители.
а) 25x^2 + 10xy + y^2 - 10x -2y
б) a^3 + a^2 - 2ab + 4b^2 +8b^3
в) x^2 + 8x - y^2 - 6y + 7
^ - степень ​

Answer 1

$a)~ 25x^2+10xy+y^2-10x-2y=25x^2+10xy+y^2-10x-2y=\ \ =left(5x+yright)^2-2left(5x+yright)=left(5x+yright)left(5x+y-2right)\ \ \ b)~ a^3+a^2-2ab+4b^2+8b^3=a^3+8b^3+a^2-2ab+4b^2=\ \ =left(a+2bright)left(a^2-2ab+4b^2right)+a^2-2ab+4b^2=left(a^2-2ab+4b^2right)left(a+2b+1right)$

$c)~ x^2+8x-y^2-6y+7=x^2+8x+16-y^2-6y-9=\ \ left(x+4right)^2-left(y+3right)^2=left(x+4-y-3right)left(x+4+y+3right)=left(x-y+1right)left(x+y+7right)$