Question

:разложите на множители 1)(m+3)^3-8 2)(x^2+1)-4x^2 3)(a^2+2ab+b^2)-c^2 4)x^2-2xc+c^2-d^2 5)x^2+2xy-m^2+y^2

Answer 1

$1)\; \; (m+3)^3-8=((m+3)-2)((m+3)^2+2(m+3)+4)=\\\\=(m+1)(m^2+6m+9+2m+6+4)=\\\\=(m+1)(m^2+8m+19)\\\\2)\; \; (x^2+1)-4x^2=1-3x^2=(1-\sqrt3x)(1+\sqrt3x)\\\\3)\; \; (a^2+2ab+b^2)-c^2=(a+b)^2=c^2=(a+b-c)(a+b+c)\\\\4)\; \; x^2-2xc+c^2-d^2=(x-c)^2-d^2=(x-c-d)(x-c+d)$

$5)\; \; x^2+2xy-m^2+y^2=(x+y)^2-m^2=(x+y-m)(x+y+m)$