Question:
Solve the following quadratic equations by factorization:
$x^{2}+2 a b=(2 a+b) x$
Solution:
We have been given
$x^{2}+2 a b=(2 a+b) x$
$x^{2}-(2 a+b) x+2 a b=0$
$x^{2}-2 a x-b x+2 a b=0$
$x(x-2 a)-b(x-2 a)=0$
$(x-2 a)(x-b)=0$
Therefore,
$x-2 a=0$
$x=2 a$
or,
$x-b=0$
$x=b$
Hence, $x=2 a$ or $x=b$.
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