Question

Разложите на множители c^2 - 1 + 2c ( c^2 - 1 ) + c^2 ( c^2 - 1 ) ; ( 3b + 1 )^2 - (3b - 2)^2 ; ( 2x - 1 )^2 - ( 4x + 1 )^2

Answer 1

$1)\; \; c^2-1+2c(c^2-1)+c^2(c^2-1)=(c^2-1)(1+2c+c^2)=\\\\=(c^2-1)(c+1)^2=(c-1)(c+1)(c+1)^2=(c-1)(c+1)^3\\\\2)\; \; (3b+1)^2-(3b-2)^2=\\\\=(3b+1-3b+2)(3b+1+3b-2)=3(6b-1)\\\\3)\; \; (2x-1)^2-(4x+1)^2=\\\\=(2x-1-4x-1)(2x-1+4x+1)=-2(x+1)\cdot 6x=\\\\=-12x(x+1)$