can you help me factor 3xy@+9xy+6x=
I don't know what the "@" stands for but one of the factors is 3x.
(3x)(y + 3y + 2)
Of course! To factor the expression 3xy^2 + 9xy + 6x, we can follow these steps:
Step 1: Look for any common factors among the terms. In this case, we can factor out the common factor of x.
The expression becomes: x(3y^2 + 9y + 6)
Step 2: Now, let's focus on the expression inside the parentheses: 3y^2 + 9y + 6.
Step 3: Check if it can be factored further. In this case, we can try factoring out a common factor of 3.
The expression becomes: x(3)(y^2 + 3y + 2)
Step 4: Next, we need to find two numbers that multiply to 2 and add up to 3 (the coefficient of y) in order to factor the trinomial (y^2 + 3y + 2).
Step 5: The numbers that satisfy these conditions are 1 and 2.
Rewrite the expression as: x(3)(y^2 + y + 2y + 2)
Step 6: Now, we can group the terms: x(3)[y(y + 1) + 2(y + 1)]
Step 7: Notice that we have a common factor of (y + 1) that we can factor out.
The expression becomes: x(3)(y + 1)(y + 2)
So, the factored form of 3xy^2 + 9xy + 6x is x(3)(y + 1)(y + 2).