To add the polynomials [tex] \tt {x}^{8} + {2x}^{4} + 1 [/tex] and [tex] \tt {2x}^{4} + {x}^{2} + 1 [/tex] let us first combine the like and unlike terms and add them :
[tex] =\tt {x}^{8} + {2x}^{4} + 1 + \tt {2x}^{4} + {x}^{2} + 1[/tex]
[tex] = \tt {x}^{2} + {x}^{2} + {x}^{2} + {x}^{2} + {2x}^{2} + {2x}^{2} + {2x}^{2} + {2x}^{2} + {x}^{2} + 1 + 1 [/tex]
[tex] =\tt {13x}^{2} + 2[/tex]
○=> Therefore :
[tex]\color{hotpink} = \tt {x}^{8} + {2x}^{4} + 1 + \tt {2x}^{4} + {x}^{2} + 1 \color{plum}= {13x}^{2} + 2[/tex]
