Solve (3b+7a)(-5a+2b): Step-by-Step Binomial Multiplication

We will use the expanded distribution law as seen below in order to simplify the given expression:

$(a+b)(c+d)=ac+ad+bc+bd$

First, we'll perform the multiplication between the pairs of parentheses using the distribution law mentioned, and then we'll combine like terms if possible. We'll do this while paying attention to the correct multiplication of signs:

$(3b+7a)(-5a+2b)= \\ -15ab+6b^2-35a^2+14ab=\\ \boxed{6b^2-ab-35a^2}$Therefore, the correct answer is answer B.