Question

Analyze the product:
x2-2ax + (a + b)(a – b)

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Answer 1

Answer:

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Step-by-step explanation:

We have

x 2−2ax+a2−b2=0

Here factors of constant term (a2−b2) are (a−b) and (a+b)

Also, Coefficient of the middle term=−2a=−[(a−b)+(a+b)]

∴x2 −2ax+a2−b2=0

⇒x2 −[(a−b)+(a+b)]x+(a−b)(a+b)=0⇒x2−(a−b)x−(a+b)x+ (a−b)(a+b)=0

⇒{x 2−(a−b)x}−{(a+b)x−(a−b)(a+b)}=0⇒

x{x−(a−b)}(a+b){x−(a−b)}=0

⇒x−(a−b)=0 or x−(a+b)=0⇒x=a−borx=a+b