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Find the HCF of (a3+b3),(a+b)2 and (a2−b2).(a^3+b^3 ),(a+b)^2 \ and\ (a^2-b^2).(a3+b3),(a+b)2 and (a2−b2).​​
Question

Find the HCF of (a3+b3),(a+b)2 and (a2b2).(a^3+b^3 ),(a+b)^2 \ and\ (a^2-b^2).​​

A.

(a+b)(a-b)

B.

(a+b)

C.

(a-b)

D.

(a3+b3)(a2b2)(a^3+b^3 )(a^2-b^2 )​​

Correct option is B

Given:

(a3+b3),(a+b)2 and (a2b2).(a^3+b^3 ),(a+b)^2 \ and\ (a^2-b^2).​​

Solution:

(a3+b3)=(a+b)(a2+b2+ab)(a+b)2=(a+b)(a+b)(a2b2)=(a+b)(ab)​(a^3 + b^3) = (a + b)(a^2 + b^2 + ab) \\ (a + b)^2 = (a + b)(a + b) \\ (a^2 - b^2) = (a + b)(a - b)
Therefore, HCF} = (a + b)


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