Question

BRAINLIEST AND HELLA POINTS An expression is shown below: 2x3y + 8xy − 4x2y − 16y Part A: Rewrite the expression by factoring out the greatest common factor. (4 points) Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

Answer 1

Answer:

$2y(x^2+4)(x-2)$

Step-by-step explanation:

$2x^{3}y+8xy-4x^2y-16y$

Part A

to know the common factor we have to get the number factor and then the variable common factor

the numbers we have

2, 8, -4, -16

we note that the greatest common factor is 2

in variables we have

$x^3y, xy, x^2y, y$

and we note is y

so we have

$2y(\frac{2x^3y}{2y}+ \frac{8xy}{2y} -\frac{4x^2y}{2y}- \frac{16y}{2y} )\\\\=2y(x^3+4x-2x^2-8)$

Part B

we can arrange conveniently as follows

$2y[(x^3-2x^2)+(4x-8)]\\\\=2y[x^2(x-2)+4(x-2)]\\\\=2y[(x-2)(x^2+4)]\\\\=2y(x^2+4)(x-2)$

Answer 2

Answer:

part b) 2x^3 y +8xy - 4x^2 y - 16y

= 2xy (x^2 + 4) - 4y (x^2 + 4)

= (2xy - 4y) (x^2 + 4)

Step-by-step explanation: