Question

If x=a-b and y=b-c, show that (a-c) (a+c-2b) =x^2-y^2

Answer 1

Step-by-step explanation:

Given, x=a-b y=b-c

RHS

x^2-y^2

=(a-b)^2 - (b-c)^2

=(a² + b² - 2ab) - ( b² + c² - 2bc)

=a² + b² - 2ab - b² - c² + 2bc

= (a² - c²)+2bc-2ab

={(a-c)(a+c)}+2b(c-a)

={(a-c)(a+c)}-2b(a-c)

=(a-c)(a+c -2b)=LHS.......Proved

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