Question

Solve the given quadratic equation by factorization method
$x^2-2ax+a^2-b^2=0$

Answer 1

We have

$x^2-2ax+a^2-b^2=0$

Here factors of constant term $(a^2-b^2)$ are $(a-b)$ and $(a+b)$

Also, Coefficient of the middle term$=-2a=-\left[\right(a-b)+(a+b\left)\right]$

$\therefore x^2-2ax+a^2-b^2=0$

$\Rightarrow x^2-\left[(a-b)+(a+b)\right]x+(a-b)(a+b)=0\Rightarrow x^2-(a-b)x-(a+b)x+(a-b)(a+b)=0$

$\Rightarrow \{x^2-(a-b\left)x\right\}-\left\{\right(a+b)x-(a-b\left)\right(a+b\left)\right\}=0\Rightarrow x\{x-(a-b\left)\right\}-(a+b)\{x-(a-b\left)\right\}=0$

$\Rightarrow x-(a-b)=0orx-(a+b)=0\Rightarrow x=a-borx=a+b$