How do you Factorize a multi variable equation, such as 2p^3 + 11p^2q + 12pq^2?
First, you find the GCF.
= p(2p^2 + 11pq + 12q^2)
= p(2p + 3q)(.......)
can you find that third factor?
To factorize a multi-variable equation like 2p^3 + 11p^2q + 12pq^2, you need to look for common factors and grouping.
Step 1: Look for common factors in each term. In this case, the only common factor is p.
2p^3 can be written as p * 2p^2
11p^2q remains the same
12pq^2 can be written as p * 12q^2
Now the equation becomes: p * 2p^2 + 11p^2q + p * 12q^2
Step 2: Group the terms with the common factor separately.
(p * 2p^2 + p * 12q^2) + 11p^2q
Step 3: Factor out the common factor from each group.
p(2p^2 + 12q^2) + 11p^2q
Step 4: Simplify the expression if possible. In this case, we can factor out 2 from the first group.
2p(p^2 + 6q^2) + 11p^2q
So, the factored form of the equation 2p^3 + 11p^2q + 12pq^2 is 2p(p^2 + 6q^2) + 11p^2q.