Question

Разложите на множители

ax^2+2ax+a

Answer 1

$<var>ax^2+2ax+a = a(x^2+2x+1) = a(x+1)^2</var>$

Answer 2

$<var>ax^{2}+2ax+a=a(x^{2}+2x+1)=a(x+1)(x+1)=a(x+1)^{2}\\\\ x^{2}+2x+1=0\\ D=b^{2}-4ac=2^{2}-4\cdot1\cdot1=0\\ x_{1,2}=\frac{-b}{2a}=\frac{-2}{2}=-1\\\\ (x+1)(x+1)=0</var>$