Question

Encuentra el término que se debe sumar o restar al trinomio dado para que sea un trinomio cuadrado
perfecto.

Answer 1

Explicación paso a paso:

${x}^{8} + 9 {x}^{4} + 25 \\ = \\ {x}^{8} + 9 {x}^{4} + {x}^{4} + 25 - {x}^{4} \\ = ( {x}^{8} + 10 {x}^{4 } + 25) - {x}^{4} \\ = ( { {x}^{4} + 5) }^{2} - {x}^{4} \\ = (( {x}^{4} + 5) + {x}^{2} )(( {x}^{4} + 5) - {x}^{2} ) \\ = ( {x}^{4} + {x}^{2} + 5)( {x}^{4} - {x}^{2} + 5)$

${m}^{6} + 8 {m}^{3} n + 36 {n}^{2} \\ = ({m}^{6} + 8 {m}^{3} n + 4 {m}^{3} n + 36 {n}^{2}) - 4 {m}^{3}n \\ = ( {m}^{6} + 12 {m}^{3} n + 36 {n}^{2} ) - 4 {m}^{2} n \\ = ( { {m}^{3} + 6n) }^{2} - 4 {m}^{2} n \\ = (( {m}^{3} + 6 {n}) + 2m \sqrt{n} )(( {m}^{3} + 6n) - 2m \sqrt{n} ) \\ = ( {m}^{3} + 2m \sqrt{n} + 6n)( {m}^{3} - 2m \sqrt{n} + 6n)$