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show that (a-b) is a factor of (a+b) 3 - (a-b) 3 -8ab 2

show that (a-b) is a factor of (a+b)3- (a-b)3-8ab2

Grade:10

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
7 years ago
Hello Student, Please find the trick to solve the question
define a polynomial in 'a' like this f(a)= (a+b)^3- (a-b)^3-8ab^2
Now check the value of f(b)= (b+b)^3- (b-b)^3-8b*b^2 = 0
since f(b)=0
Therefore , a=b is the root of f(a)
Implies a-b is a factor

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