Question

2v^3 w^4 -2v^3 factor completely

Answer 1

To factor the expression 2v^3 w^4 - 2v^3 completely, we can first factor out the common factor of 2v^3. Then, we use the difference of squares to further factor the expression.

Step-by-step explanation:

The given expression is 2v^3 w^4 - 2v^3. To factor it completely, we can factor out the common factor of 2v^3 from both terms:

2v^3 w^4 - 2v^3 = 2v^3 (w^4 - 1).

Now we can further factor the expression inside the parentheses as the difference of squares:

w^4 - 1 = (w^2)^2 - 1^2 = (w^2 - 1)(w^2 + 1).

Therefore, the completely factored form of the expression is 2v^3 (w^2 - 1)(w^2 + 1).