Final answer:
To factor the expression 45w²-20w⁴ completely, factor out the greatest common factor of 5w² to get 5w² (9 - 4w²), then factor the difference of squares to obtain the final expression 5w²(3 + 2w)(3 - 2w).
Step-by-step explanation:
The question asks to factor the expression 45w²-20w⁴ completely.
To start, we can factor out the greatest common factor (GCF) from both terms. Both terms have a factor of 5w², so we can factor that out:
5w² (9 - 4w²)
Next, notice that the expression inside the parentheses is a difference of squares, as 9 is 3² and 4w² is (2w)².
We can factor this further into:
5w²(3 + 2w)(3 - 2w)
This is the completely factored form of the original expression.