Final answer:
To simplify the given expression, we first simplify the expression inside the parentheses by dividing (4b³ - 25b²) by 14b. Then, we distribute the -(1/14) factor and combine like terms to get the final simplified expression.
Step-by-step explanation:
To simplify the given expression, we follow the order of operations: parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
First, we simplify the expression inside the parentheses:
4b³ - 25b²/14b - 2 = (4b³ - 25b²)/(14b) - 2
Next, we divide (4b³ - 25b²) by 14b:
(4b³ - 25b²)/(14b) = (1/14)(4b³ - 25b²)
Substituting the simplified expression back into the original expression:
4 - [(1/14)(4b³ - 25b²)] - b²
Now, we distribute the -(1/14) factor:
4 - (1/14)(4b³ - 25b²) - b²
= 4 - (1/14)(4b³) + (1/14)(25b²) - b²
= 4 - (4/14)b³ + (25/14)b² - b²
= 4 - (4/14)b³ + (25/14 - 1)b²
= 4 - (2/7)b³ + (11/14)b²
Finally, combine like terms:
= 4 - (2/7)b³ + (11/14)b² - b²
Simplifying further, we get:
= 4 - (2/7)b³ + (11/14 - 1)b²
= 4 - (2/7)b³ + (11/14)(-1/1)b²
= 4 - (2/7)b³ - (11/14)b²
This is the simplified expression.