Question
Solve equation by factorization : $a^2x^2 + (a^2+ b^2)x + b^2 = 0, a \neq 0$
✓
Answer
$a^2 x^2+\left(a^2+b^2\right) x+b^2=0$
$ \Rightarrow a^2 x(x+1)+b^2(x+1)=0$
$ \Rightarrow(x+1)\left(a^2 x+b^2\right)=0$
$ \Rightarrow(x+1)=0, \text { then } x=-1$
or
$a^2 x+b^2=0 \text {, then } a^2 x=-b^2 \text {. }$
$\Rightarrow x =\frac{-b^2}{a^2}$
Hence $x =-1, \frac{-b^2}{a^2}$.
$ \Rightarrow a^2 x(x+1)+b^2(x+1)=0$
$ \Rightarrow(x+1)\left(a^2 x+b^2\right)=0$
$ \Rightarrow(x+1)=0, \text { then } x=-1$
or
$a^2 x+b^2=0 \text {, then } a^2 x=-b^2 \text {. }$
$\Rightarrow x =\frac{-b^2}{a^2}$
Hence $x =-1, \frac{-b^2}{a^2}$.
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