Question

Which polynomial represents the sum below (x^8 + 2x^4 + 1) + (2x^4 + x^2 + 1)

Answer 1

To add the polynomials
`\tt {x}^(8) + {2x}^(4) + 1` and
`\tt {2x}^(4) + {x}^(2) + 1` let us first combine the like and unlike terms and add them :

`=\tt {x}^(8) + {2x}^(4) + 1 + \tt {2x}^(4) + {x}^(2) + 1`

`= \tt {x}^(2) + {x}^(2) + {x}^(2) + {x}^(2) + {2x}^(2) + {2x}^(2) + {2x}^(2) + {2x}^(2) + {x}^(2) + 1 + 1`

`=\tt {13x}^(2) + 2`

○=> Therefore :

`\color{hotpink} = \tt {x}^(8) + {2x}^(4) + 1 + \tt {2x}^(4) + {x}^(2) + 1 \color{plum}= {13x}^(2) + 2`