# Solve the following differential equation by factorization method. x^{2}-2ax+a^{2}-b^{2}=0

Solve the following differential equation by factorization method.
${x}^{2}-2ax+{a}^{2}-{b}^{2}=0$
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Step 1
The given quadratic equation is, ${x}^{2}-2ax+{a}^{2}-{b}^{2}=0$
Step 2
2a is written as, 2a=(a+b)+(a-b) and ${a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)$
${x}^{2}-\left(\left(a+b\right)+\left(a-b\right)\right)x+\left(a+b\right)\left(a-b\right)=0$
${x}^{2}-\left(a+b\right)x-\left(a-b\right)x+\left(a+b\right)\left(a-b\right)=0$
x(x-(a+b))-(a-b)(x-(a+b))
(x-(a+b))(x-(a-b))
x-(a+b)=0, x-(a-b)=0
x=(a+b), x=(a-b)
x=a+b, x=a-b
This is the solution of the quadratic equation is, ${x}^{2}-2ax+{a}^{2}-{b}^{2}=0$
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Louis Page
Step 1
Given quadratic equation is ${x}^{2}-2ax+{a}^{2}{b}^{2}=0$
Factorizing the given equation is
${x}^{2}-\left(a+b\right)x-\left(a-b\right)x+{a}^{2}-{b}^{2}=0$
x(x-(a+b))-(a-b)(x-(a+b))=0
(x-(a+b))(x-(a-b))=0
x=(a+b), (a-b)
Step 2
Hence obtained