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Polynomial identities


Felix was asked whether the following equation is an identity:
He performed the following steps:
=(x2+1)2Step 1=x4+x2+x2+1Step 2=x4+2x2+1Step 3=x4+2x2+12x2+2x2Step 4=(x42x2+1)+4x2Step 5=(x21)2+(2x)2
For this reason, Felix stated that the equation is a true identity.
Is Felix correct? If not, in which step did he make a mistake?
Choose 1 answer: