Question

Factor the expression 2x4y – 18x2y3 completely.

Answer 1

Answer:

B. 2x2y(x – 3y)(x + 3y)

Step-by-step explanation:

$2 {x}^{4} y - 18 {x}^{2} {y}^{3} \\ = 2 {x}^{2} y( {x}^{2} - 9 {y}^{2} ) \\ = 2 {x}^{2} y \{ {x}^{2} - {(3y)}^{2} \} \\ \purple {\boxed{ \bold{ = 2 {x}^{2} y(x - 3y)(x + 3y)}}}$

Answer 2

Answer:

B

Step-by-step explanation:

$2x^{4}y - 18x^{2}y^{3}$

Both sides have $x^{2}$

$x^{2} (2x^{2}y - 18y^{3})$

Both sides have y

$yx^{2} (2x^{2} - 18y^{2})$

Both sides have 2

$2yx^{2} (x^{2} - 9y^{2})$

• Rule : $x^{2} - y^{2} = (x+y)(x -y)$

$x^{2} = x.x\\9y^{2} = 3y. 3y$

$(x^{2} - 9y^{2}) = (x +3y) (x-3y)$

Final:

$\red{ 2 {x}^{2} y(x - 3y)(x + 3y)}$

Hope this helps ^-^