How do you factorise x^4-x^2y-6y^2
(x^2 - 3y)(x^2 + 2y)
x^4-x^2y-6y^2
= x^2(x^2-y)-6y^2
or
= x^4-y(x^2+6y)
There's no way to make it a product of just two factors
To factorize the expression x^4 - x^2y - 6y^2, we can use a technique called factorization by grouping. Here are the steps to solve it:
Step 1: Look for common factors, if any. In this case, there are no common factors among the terms, so we move to the next step.
Step 2: Group the terms. We will group the terms in pairs to look for common factors within each pair. Let's group the terms as follows:
(x^4) - (x^2y) - (6y^2)
Step 3: Factor out the common factors within each group. Let's factor out x^2 from the first group and -y from the second group:
x^2(x^2 - y) - y(6y)
Now we have:
x^2(x^2 - y) - 6y^2
Step 4: Look for any common factors between the two groups. In this case, there are no common factors, so we move to the next step.
Step 5: Combine the factored groups.
x^2(x^2 - y) - 6y^2
So, the factorized form of the expression x^4 - x^2y - 6y^2 is:
(x^2 - 6y^2)(x^2 - y)
Therefore, x^4 - x^2y - 6y^2 can be factorized as (x^2 - 6y^2)(x^2 - y).