x^2+9xy+20y^2

i never deal with something like this before i come up with (x+4)(x+5) but that wrong because y have to be there how i do this?

All you had to do was include a y at the end of each binomial

(x+4y)(x+5y)

(expand it to prove the answer is correct)

oh i get it :D thanks very much reiny :)

To factor the expression x^2 + 9xy + 20y^2, you can use a technique called "factoring by grouping." Here's how you can do it:

Step 1: Observe the signs of the coefficients. In this case, all the signs are positive.

Step 2: Multiply the coefficient of x^2 (which is 1) with the constant term (which is 20y^2). So, 1 * 20y^2 = 20y^2.

Step 3: Now, think about two numbers that add up to 9 (the coefficient of xy) and multiply to give you 20y^2. In this case, the numbers are 4y and 5y.

Step 4: Rewrite the middle term (9xy) by splitting it into the sum of 4xy and 5xy. Your expression now becomes:
x^2 + 4xy + 5xy + 20y^2.

Step 5: Group the terms: (x^2 + 4xy) + (5xy + 20y^2).

Step 6: Factor out the common terms from each group. In the first group, you can factor out x, and in the second group, you can factor out 5y. The expression now becomes:
x(x + 4y) + 5y(x + 4y).

Step 7: Notice that you now have a common factor of (x + 4y) in both terms. Factor it out: (x + 4y)(x + 5y).

Therefore, the factored form of the expression x^2 + 9xy + 20y^2 is (x + 4y)(x + 5y).