Respuesta :

Solution:

Finding the GCF of both terms:

  • 121x⁴y⁶: 1, 11, 121, x⁴, y⁶
  • 25x²z¹²: 1, 5, 25, x², z¹²

GCF = x²

Factorizing both the terms:

  • 121x⁴y⁶ - 25x²z¹²
  • => x²(121x²y⁶ - 25z¹²)      [Taking out x² as it is common in both terms]

Further factorizing:

  • => x²(11xy³ - 5z⁶)(11xy³ + 5z⁶)

The factorized binomial is x²(11xy³ - 5z⁶)(11xy³ + 5z⁶).

[tex] \sf \to \: 121 {x}^{4} {y}^{6} - 25 {x}^{2} {z}^{12} [/tex]

Factor out x² from the expression

[tex] \sf \to \: {x}^{2} \times (121 {x}^{2} {y}^{6} - 25 {z}^{12} )[/tex]

Use the identity a²- b²= (a-b)(a+b) to factor the expression

  • a = 11xy³
  • b = 5z⁶

[tex] \sf \to {x}^{2} \times ( {11xy}^{3} - 5 {z}^{6} ) \times ( {11xy}^{3} + {5z}^{6} )[/tex]

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