Generate an expression equivalent to: 5+6b+12c+10b−4c−2. In the simplest form of the equivalent expression, what is the coefficient of variable b? $$

Question

Generate an expression equivalent to: 5+6b+12c+10b−4c−2. In the simplest form of the equivalent expression, what is the coefficient of variable b? $$

Answer 1

The coefficient of the variable b is obtained by adding all the terms containing b together.

5 + 6b + 12c + 10b - 4c - 2

Combining like terms:
(6b + 10b) + (5 + 12c - 4c) - 2

Simplifying:
16b + (5 + 12c - 4c) - 2
16b + 5 + 12c - 4c - 2

Further simplifying:
16b + 5 + 12c - 4c - 2
16b + 3 + 12c - 4c

So, the coefficient of the variable b in the simplest form of the equivalent expression is 16.