Respuesta :

Hrishii

Answer:

B. 2x2y(x – 3y)(x + 3y)

Step-by-step explanation:

[tex]2 {x}^{4} y - 18 {x}^{2} {y}^{3} \\ = 2 {x}^{2} y( {x}^{2} - 9 {y}^{2} ) \\ = 2 {x}^{2} y \{ {x}^{2} - {(3y)}^{2} \} \\ \purple {\boxed{ \bold{ = 2 {x}^{2} y(x - 3y)(x + 3y)}}}[/tex]

merue

Answer:

B

Step-by-step explanation:

[tex]2x^{4}y - 18x^{2}y^{3}[/tex]

Both sides have [tex]x^{2}[/tex]

[tex]x^{2} (2x^{2}y - 18y^{3})[/tex]

Both sides have y

[tex]yx^{2} (2x^{2} - 18y^{2})[/tex]

Both sides have 2

[tex]2yx^{2} (x^{2} - 9y^{2})[/tex]

  • Rule : [tex]x^{2} - y^{2} = (x+y)(x -y)[/tex]

[tex]x^{2} = x.x\\9y^{2} = 3y. 3y[/tex]

[tex](x^{2} - 9y^{2}) = (x +3y) (x-3y)[/tex]

Final:

[tex]\red{ 2 {x}^{2} y(x - 3y)(x + 3y)}[/tex]

Hope this helps ^-^

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