Multiply. Give your answer in standard form.
(3n^2+2n+4)(2n-1)
6n^3 + n^2 - 6n + 4
To multiply the given expression (3n^2 + 2n + 4) and (2n - 1), we can apply the distributive property. Let's break it down step-by-step:
Step 1: Multiply the first terms of both expressions.
(3n^2)(2n) = 6n^3
Step 2: Multiply the first term of the first expression by the constant in the second expression.
(3n^2)(-1) = -3n^2
Step 3: Multiply the constant in the first expression by the second term in the second expression.
(2)(2n) = 4n
Step 4: Multiply the constant in both expressions.
(2)(-1) = -2
Step 5: Combine all the terms obtained in the previous steps.
6n^3 - 3n^2 + 4n - 2
Therefore, the product of (3n^2 + 2n + 4)(2n - 1) is 6n^3 - 3n^2 + 4n - 2 in standard form.