Question
The HCF of a^6 - 1 and a^4+ 2a^3- 2a-1 is
Solution
a^6- 1 = (a^2)³ - 1³ Using the formula, x³-y³=(x-y)(x^2+ y^2+xy) (a^2)³ - 1³ = (a^2- 1) (a^4+ 1+ a^2 ×1) = (a^2- 1) (a^4+ 1+ a^2) ......................................(i) a^4+ 2a³-2a-1 = a^(4 )– 1+2a(a^2- 1) = (a^2)²- 1²+2a(a^2- 1) = (a^2 + 1) (a²-1) +2a(a^2- 1) = (a^2- 1) (a^2 + 1 +2a) ..........................................(ii) From equation (i) and (ii) HCF is the common term = a^2- 1
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