Factor completely
81a2 + 36a + 4
(9a +2)^2
If you mean
81a^2 + 36a + 4 then it looks like a perfect square to me, and it factors to
(9a+2)(9a+2) or (9a+2)^2
To factor completely, we need to find the factors of each term in the expression and look for common factors that can be factored out. Let's factor the given expression step by step:
First, let's factor out the greatest common factor (GCF) of the coefficients. The GCF of 81, 36, and 4 is 1. However, each term has an "a" term in common. So, we can factor out an "a" term as well.
Taking out the common factor, we have:
1a(81a + 36 + 4)
Next, let's simplify the expression within the parentheses:
1a(81a + 40)
Now, we can see that the expression inside the parentheses is a binomial with the form of "ax + b" where a = 81 and b = 40. To factor this further, we need to find two numbers whose product is equal to the product of a and b (i.e., 81 * 40 = 3240) and whose sum is equal to the coefficient of the middle term (i.e., 81).
Let's find those numbers:
The factors of 3240 are:
1, 3240
2, 1620
3, 1080
4, 810
5, 648
6, 540
8, 405
9, 360
10, 324
12, 270
15, 216
18, 180
20, 162
24, 135
27, 120
30, 108
36, 90
40, 81
From these factors, we can see that the numbers we are looking for are 40 and 81.
Therefore, the factored form of the expression 81a^2 + 36a + 4 is:
1a(40a + 81)