factorise p^2+q^2+2q-6q^2+3pq+4yz
p(p+3q)+q^2(1+2q-2)+4yz
after successful factoring, we should only see one term
The above answer contains 3 terms, so it is not factored completely.
In the given question, the 4yz messes everything.
The expression cannot be factored.
To factorize the expression p^2+q^2+2q-6q^2+3pq+4yz, we need to look for common factors and rearrange the terms.
Step 1: Group the terms with common factors.
The terms involving 'q' are q^2+2q and -6q^2. Factor out the common factor 'q' from these terms: q(q+2) - 6q^2.
Step 2: Now let's group the remaining terms.
The terms involving 'p' are p^2 and 3pq. Factor out the common factor 'p' from these terms: p(p+3q).
Step 3: Group the terms with 'yz'.
We have the term 4yz, which does not have any common factor with the previous terms. So it stands as it is.
Putting all the simplified terms together, we get:
(q+2)(-6q) + p(p+3q) + 4yz
To further simplify the equation, multiply (-6q) by each term inside the first set of parentheses:
(-6q)(q+2) + p(p+3q) + 4yz
Now distribute the -6q:
-6q^2 - 12q + p(p + 3q) + 4yz
So, the fully factorized form of the expression p^2+q^2+2q-6q^2+3pq+4yz is:
-6q^2 - 12q + p(p + 3q) + 4yz