Question

Розклади на множники вирази: 1+6х+9х^2; 36у^2+12у+1; -4с^2-4c-1;

Answer 1

$\displaystyle \tt 1+6x+9x^2=1^2+2\cdot1\cdot3x+3^2x^2=1^2+2\cdot1\cdot3x+(3x)^2=(1+3x)^2=\bold{(1+3x)(1+3x)}$

$\displaystyle \tt 36y^2+12y+1=6^2y^2+2\cdot6\cdot1+1^2=(6y)^2+2\cdot6y\cdot1+1^2=(6y+1)^2=\bold{(6y+1)(6y+1)}$

$\displaystyle \tt -4c^2-4c-1=-4c^2-2c-2c-1=-2c(2c+1)-(2c+1)=\bold{-(2c+1)(2c+1)}$