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

Solve the following equation:

$(3b+7a)\cdot(-5a+2b)=\text{?}$

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 will proceed to combine like terms if possible. We'll do this whilst observing 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.