Factorise. 7ab-2b^2+4a^2

4a^2 + 7ab - 2b^2

Find the two factors for each end term (4,1)(2,1), whose products will add to the middle term. Watch the signs.

To factorize the expression 7ab - 2b^2 + 4a^2, we need to look for common factors in each term.

Step 1: Identify any common factors among the terms.
In this expression, the only common factor is 1 (since all the terms have the variables a and b, but no numerical factors).

Step 2: Group the terms accordingly.
Group the terms in pairs if they have common factors. In this case, we can group the first two terms (7ab and -2b^2) since they both have a common factor of b. We don't need to group the third term (4a^2) separately.

7ab - 2b^2 + 4a^2
can be rearranged as
(7ab - 2b^2) + 4a^2

Step 3: Factor out the common factor from each group.
From the grouped terms (7ab - 2b^2) and 4a^2, we can extract the common factors.
The common factor in the first group is b:
b(7a - 2b) + 4a^2

Step 4: Simplify the expression if possible.
The expression cannot be further simplified since there are no common factors between the terms (7a - 2b) and 4a^2).

So, the fully factorized form of 7ab - 2b^2 + 4a^2 is:
b(7a - 2b) + 4a^2