Al factorizar el trinomio cuadrado perfecto, obtenemos el siguiente resultado: (que no se como resolver) xd algun pro que sepa resolverlo?

Answer:

[tex]\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2[/tex]

Step-by-step explanation:

Trinomio Cuadrado Perfecto

El producto notable llamado cuadrado de un binomio se expresa como:

[tex](a-b)^2=a^2-2ab+b^2[/tex]

Si se tiene un trinomio, es posible convertirlo en un cuadrado perfecto si cumple con las condiciones impuestas en la fórmula:

* El primer término es un cuadrado perfecto

* El último término es un cuadrado perfecto

* El segundo término es el doble del proudcto de los dos términos del binomio.

Tenemos la expresión:

[tex]\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8[/tex]

Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:

[tex]\displaystyle a=\sqrt{\frac{100}{81}m^8p^{12}q^{16}z^2}[/tex]

[tex]\displaystyle a=\frac{10}{9}m^4p^{6}q^{8}z[/tex]

Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:

[tex]\displaystyle b=\sqrt{\frac{1}{49}m^2p^2z^8[/tex]

[tex]\displaystyle b=\frac{1}{7}mpz^4[/tex]

Nos cercioramos de que el término central es 2ab:

[tex]\displaystyle 2ab=2\frac{10}{9}m^4p^{6}q^{8}z\frac{1}{7}mpz^4[/tex]

Operando:

[tex]\displaystyle 2ab=\frac{20}{63}m^5p^7q^8z^5[/tex]

Una vez verificado, ahora podemos decir que:

[tex]\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2[/tex]

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