simplify the expression.
(2k+1)(k-4)
A: 2k^2-7k+4
B: 2k^2-3k+4
C: 2k^2+9k+4
D: 2k^2-7k-4
A: 2k^2-7k+4
To simplify the expression (2k+1)(k-4), we need to distribute the terms in the first set of parentheses to the terms in the second set of parentheses.
First, distribute 2k to both terms in the second set of parentheses:
2k * k = 2k^2
2k * -4 = -8k
Next, distribute 1 to both terms in the second set of parentheses:
1 * k = k
1 * -4 = -4
Putting it all together, we have:
(2k+1)(k-4) = 2k^2 - 8k + k - 4
Now, combine like terms:
2k^2 - 8k + k - 4 = 2k^2 - 7k - 4
Therefore, the simplified expression is: 2k^2 - 7k - 4.
The correct answer is D: 2k^2 - 7k - 4.