Solve the Following Quadratic Equation by Factorization
Question:
\[ x^2+2ab=(2a+b)x \]Solution
Bringing all terms to one side:
\[ x^2-(2a+b)x+2ab=0 \]We need two terms whose sum is \((2a+b)\) and product is \(2ab\).
\[ 2a+b=(2a)+b \] \[ (2a)\times b=2ab \]Splitting the middle term:
\[ x^2-2ax-bx+2ab=0 \]Taking common factors:
\[ x(x-2a)-b(x-2a)=0 \] \[ (x-2a)(x-b)=0 \]Therefore,
\[ x-2a=0 \quad \text{or} \quad x-b=0 \] \[ x=2a \quad \text{or} \quad x=b \]