How do I simplify (2a - b)(4a^2 - 2ab + b^2)? I keep getting 8a^3 - 8a^2b + 4ab^2 - b^3, but it shows wrong.
That's what I get, too.
To simplify the expression (2a - b)(4a^2 - 2ab + b^2), you need to apply the distributive property. This property tells us that when we multiply a sum by another term, we need to multiply each term individually and then combine like terms.
Let's go step by step:
Step 1: Multiply 2a by each term inside the second parentheses:
2a * 4a^2 = 8a^3
2a * (-2ab) = -4a^2b
2a * b^2 = 2ab^2
Step 2: Multiply -b by each term inside the second parentheses:
-b * 4a^2 = -4a^2b
-b * (-2ab) = 2ab^2
-b * b^2 = -b^3
Now combine the like terms obtained:
8a^3 - 4a^2b + 2ab^2 - 4a^2b + 2ab^2 - b^3
Now combine the like terms:
8a^3 - 8a^2b + 4ab^2 - b^3
So, your answer, 8a^3 - 8a^2b + 4ab^2 - b^3, is correct. If it shows as incorrect, please double-check your calculations or refer to the answer key for the specific instructions given.