Factor the following trinomial: w^18 – 9w^9y^5 + 14y^10
(w^9 - 2y^5)(w^9 - 7y^5)
Factor completely.
49t6 - 4k8
factor completely 49t6 - 4k8
w^18-9w^9y^5+14y^10
factor the following trinomial, this can be factored similar to a quadric
To factor the trinomial w^18 – 9w^9y^5 + 14y^10, let's first look for any common factors among the terms.
The only common factor we can see is 1, so let's move on to factoring the trinomial. Since each term contains different variables raised to different powers, the trinomial cannot be factored further by taking out any common factors.
To factor the trinomial, we can try factoring by grouping. Here's how:
1. Split the middle term –9w^9y^5 into two terms such that the sum of the two terms is –9w^9y^5 and their product is 14y^10. We can write:
–9w^9y^5 = –2w^9y^5 – 7w^9y^5
2. Now, group the terms:
w^18 – 2w^9y^5 – 7w^9y^5 + 14y^10
3. Factor out the greatest common factor (GCF) from each group:
w^9(w^9 – 2y^5) – 7y^5(w^9 – 2y^5)
4. Notice that we have a common binomial term, (w^9 – 2y^5), so we can factor it out:
(w^9 – 2y^5)(w^9 – 7y^5)
Therefore, the factored form of the trinomial w^18 – 9w^9y^5 + 14y^10 is (w^9 – 2y^5)(w^9 – 7y^5).