Question

помогите все 3 задания​

Answer 1

Ответ:

1005. $ab^{2} -a-b^{3} +b=a(b^{2} -1)-b(b^{2} -1)=(b^{2} -1)(a-b)=(b-1)(b+1)(a-b)$

$bx^{2} +2b^{2} -b^{3} -2x^{2} =b(x^{2} -b^{2} )-2(-b^{2}+x^{2} )=(x^{2} -b^{2} )(b-2)=(x-b)(x+b)(b-2)$

$x^{3} +x^{2} y-4y-4x=x^{2} (x+y)-4(y+x)=(x+y)(x^{2} -4)=(x+y)(x-2)(x+2)$

$x^{3} -3y^{2} +3x^{2} -xy^{2} =x^{2} (x+3)-y^{2} (3+x)=(x+3)(x^{2} -y^{2} )=(x+3)(x-y)(x+y)$

1006.

$a)x^{3} -x=0\\x(x^{2} -1)=0\\x1=0\\x^{2} -1=0\\x^{2} =1\\x2=1\\x3=-1$

$b)9x-x^{3} =0\\x(9-x^{2} )=0\\x1=0\\9-x^{2} =0\\-x^{2} =-9\\x^{2} =9\\x2=3\\x3=-3$

$c)x^{3} +x^{2} =0\\x^{2} (x+1)=0\\x^{2} =0\\x1=0\\x+1=0\\x2=1\\x3=-1$

$d)5x^{4} -20x^{2} =0\\5x^{2} (x^{2} -4)=0\\x^{2} (x^{2} -4)=0\\x^{2} =0\\x1=0\\x^{2} -4=0\\x2=2\\x3=-2$

1007.

$a)x^{3} +x=0\\x(x^{2} +1)=0\\x1=0\\x^{2} +1=0\\x^{2} =-1\\\neq$

$x^{3} -2x^{2} =0\\x^{2} (x-2)=0\\x^{2} =0\\x1=0\\x-2=0\\x2=2$

Объяснение: