Α²+7ab+10b² factor with 2 variables

So we need to find what multiplies to 10 and adds to 7. The most immediate answer is 5 and 2. Though we have two variables, the factored portion is mostly the same.
Your answer should come out as:

(a+5b)(a+2b)

You may distribute to check the

Once distributed, they multiply to:
a^2+7ab+b^2
Which is the original question, so it checks out.

I hope this Helps!