factor 6x^2+17xy+12y^2
this is your answered when completely factored for 100% sure (3x+4y) (2x+3y)
To factor the expression 6x^2 + 17xy + 12y^2, we need to look for two binomials that multiply together to give us the original expression.
Step 1: Look for two numbers that multiply together to give us the product of the coefficient of x^2 (6) and y^2 (12). In this case, the numbers are 2 and 3, since 2 * 3 = 6 and 2 * 3 = 12.
Step 2: Break down the middle term (17xy) using the two numbers we found in Step 1. We want to rewrite 17xy using these two numbers in a way that allows us to factor by grouping.
17xy can be rewritten as (2xy) + (15xy) since 2xy * 15xy = 30x^2y^2, and 2xy + 15xy = 17xy.
Step 3: Now we can rewrite the original expression as follows:
6x^2 + 2xy + 15xy + 12y^2
Step 4: Group the terms and look for a common factor between the terms in each group:
(6x^2 + 2xy) + (15xy + 12y^2)
In the first group, the common factor is 2x:
2x(3x + y)
In the second group, the common factor is 3y:
3y(5x + 4y)
Step 5: Now, we have factored the expression completely:
(2x + 3y)(3x + 4y)
So, the factored form of 6x^2 + 17xy + 12y^2 is (2x + 3y)(3x + 4y).