Question

Multiply the linear expression.

(0.6b−4.2)12.5b

Answer 1

To multiply the linear expression \( (0.6b - 4.2) \) by \( 12.5b \), we will apply the distributive property:

\[
(0.6b - 4.2) \cdot 12.5b = 0.6b \cdot 12.5b - 4.2 \cdot 12.5b
\]

Now, we can calculate each term separately:

1. \( 0.6b \cdot 12.5b \):
\[
0.6 \cdot 12.5 = 7.5 \quad \text{and} \quad b \cdot b = b^2
\]
Thus, \( 0.6b \cdot 12.5b = 7.5b^2 \).

2. \( -4.2 \cdot 12.5b \):
\[
-4.2 \cdot 12.5 = -52.5
\]
Thus, \( -4.2 \cdot 12.5b = -52.5b \).

Putting it all together, we get:

\[
(0.6b - 4.2) \cdot 12.5b = 7.5b^2 - 52.5b
\]

So the final answer is:

\[
\boxed{7.5b^2 - 52.5b}
\]