Question

factor completely.
$2m^{5}+32m^{2}-4m^{4}-16m^{3}$

Explanation:

Step1: Group terms

Group the first two terms and the last two terms:
$$(2m^5 - 4m^4) + (32m^2 - 16m^3)$$

Step2: Factor out GCF from each group

Factor out $2m^4$ from the first group and $16m^2$ from the second group:
$$2m^4(m - 2) - 16m^2(m - 2)$$

Step3: Factor out common binomial factor

Factor out $(m - 2)$:
$$(m - 2)(2m^4 - 16m^2)$$

Step4: Factor out GCF from the second factor

Factor out $2m^2$ from $2m^4 - 16m^2$:
$$(m - 2) \cdot 2m^2(m^2 - 8)$$

Step5: Rearrange and simplify

Rearrange the factors:
$$2m^2(m - 2)(m^2 - 8)$$

Answer:

$2m^2(m - 2)(m^2 - 8)$