12a^2b over 4 times 4a+8b over 20a^2b^3
To simplify the expression (12a^2b)/(4) * (4a+8b)/(20a^2b^3), we can follow these steps:
Step 1: Simplify within each fraction separately.
In the first fraction, 12a^2b divided by 4 can be simplified as 3a^2b.
In the second fraction, 4a+8b divided by 20a^2b^3 can be simplified as (a + 2b)/(5a^2b^3).
Step 2: Combine the two fractions.
Now we have the expression (3a^2b) * ((a + 2b)/(5a^2b^3)). To multiply these fractions, we multiply the numerators together and the denominators together.
Multiplying the numerators: 3a^2b * (a + 2b) = 3a^3b + 6a^2b^2
Multiplying the denominators: 5a^2b^3
Step 3: Simplify the result.
The final simplified expression is (3a^3b + 6a^2b^2)/(5a^2b^3).
Remember, when simplifying expressions, we can cancel out common factors (e.g., numerator and denominator both have a^2b in this case), but we cannot cancel out different terms (e.g., a cannot be canceled out with a^2).