Question

3- Calculo el MCD y MCM de los siguientes polinomios a) m² + 2mn + n²/m4 – n4 -
b) a? - 25 / a2 + 2a - 15 -​

Answer 1

Verified answer

[tex]\mathrm{Encontrar\:el\:maximo\:comun\:divisor\:de\:}m^4-n^4[/tex]

[tex]\bold{m^4-n^4}[/tex]

[tex]\bold{=\left(m^2\right)^2-\left(n^2\right)^2}[/tex]

[tex]\bold{=\left(m^2+n^2\right)\left(m^2-n^2\right)}[/tex]

[tex]\bold{=\left(m^2+n^2\right)\left(m+n\right)\left(m-n\right)}[/tex]

[tex]\mathrm {Factor \: comun:}[/tex]

[tex]\boxed{\bold{\left(m+n\right)\cdot \left(m-n\right)\cdot \left(m^2+n^2\right)}}[/tex]

↑↑↑↑

MCD

[tex]\mathrm{Encontrar\:el\:minimo\:comun\:multiplo\:de\:}m^4-n^4[/tex]

[tex]\bold{m^4-n^4}[/tex]

[tex]\bold{=\left(m^2\right)^2-\left(n^2\right)^2}[/tex]

[tex]\bold{=\left(m^2+n^2\right)\left(m+n\right)\left(m-n\right)}[/tex]

[tex]\mathrm{Multiplica \: cada \: factor \: con \: la \: mayor \: potencia:}[/tex]

[tex]\boxed{\bold{\left(m+n\right)\cdot \left(m-n\right)\cdot \left(m^2+n^2\right)}}[/tex]

↑↑↑↑

MCM