Not sure of this one. Factor completley
1-81z^2
and this on
16p^2q^2-8pq^2+q^2
To factor completely, we need to find the common factors of each expression and then look for any patterns or possibilities for further factoring.
1. Factor completely: 1 - 81z^2
First, observe that 1 is a perfect square, which means it cannot be factored further.
Now, let's focus on 81z^2. We can rewrite it as (9z)^2 since (9z)^2 equals 81z^2.
Applying the difference of squares formula: a^2 - b^2 = (a + b)(a - b), we can factor 1 - 81z^2 as follows:
1 - 81z^2 = 1 - (9z)^2
= (1 + 9z)(1 - 9z)
Hence, 1 - 81z^2 can be factored completely as (1 + 9z)(1 - 9z).
2. Factor completely: 16p^2q^2 - 8pq^2 + q^2
Notice that the expression consists of three terms, and none of them have any common factor, so we cannot factor the expression using common factors.
In this case, we'll look for any patterns or possibilities for grouping. Arranging them, we have:
(16p^2q^2) - (8pq^2) + (q^2)
Now, let's focus on the first two terms, 16p^2q^2 and 8pq^2. They have a common factor of 8pq^2. We can factor it out:
= 8pq^2(2p - 1) + q^2
Now, we have 8pq^2(2p - 1) + q^2. Since there are no common factors between these terms, we cannot factor further.
Hence, 16p^2q^2 - 8pq^2 + q^2 is factored as 8pq^2(2p - 1) + q^2.