factor completely x^2+6xy+8y^2

Dont 4 and 2 add to six, multiply to 8?

Got it, thanks

To factor the given expression, x^2 + 6xy + 8y^2, we can use the concept of factoring a quadratic trinomial. Here's how you can do it step by step:

Step 1: Look for common factors, if any:
In this case, there are no common factors among the three terms.

Step 2: Identify the pattern:
Notice that the expression has the form of a quadratic trinomial, ax^2 + bx + c, where a = 1, b = 6xy, and c = 8y^2.

Step 3: Find two numbers whose product is equal to a*c and the sum is equal to b:
Here, a*c = 1 * 8y^2 = 8y^2, and b = 6xy.
We need to find two numbers, let's say m and n, such that mn = 8y^2 and m + n = 6xy.

Step 4: Break down the middle term using the two numbers found:
Since mn = 8y^2, we can rewrite the middle term, 6xy, as mxy + nxy.

Step 5: Re-group the expression:
Now, we can re-group the terms in order to factor by grouping.
x^2 + mxy + nxy + 8y^2 can be written as x^2 + (mxy + nxy) + 8y^2.

Step 6: Factor by grouping:
Now, we can factor the expression by grouping:
(x^2 + mxy) + (nxy + 8y^2)

In the first group, we can factor out the greatest common factor (GCF), which is x:
x(x + my) + (nxy + 8y^2)

In the second group, we can factor out the greatest common factor (GCF), which is y:
x(x + my) + y(nx + 8y)

Step 7: Factor out any common factors left:
Since (x + my) is a common factor to both terms, we can factor it out:
(x + my)(1 + ny)

Therefore, the fully factored form of the expression x^2 + 6xy + 8y^2 is (x + my)(1 + ny).