Find the HCF of a3 + 1 +2a2 + 2a, a3 - 1 and a4 + a2 + 1
1 Answer
Solution:
Here, first expression is
a3 + 1 +2a2 + 2a
= a3 + 13 + 2a(a+1)
= (a+1)(a2 - a +1) + 2a(a+1)
= (a+1) (a2 - a +1 + 2a)
= (a+1) (a2 + a +1)
Second expression,
= a3 - 1
= a3 - 13
= (a-1)(a2 + a +1)
Third expression,
a4 + a2 + 1
= (a2)2 + (1)2 + a2
= (a2 + 1)2 - 2a2 + a2
= (a2 + 1)2 - a2
= (a2 + a +1) (a2 - a +1)
Hence highest common factor (HCF) from all three expressions is (a2 + a +1)
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