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 :

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