Simplify the expression.
(2k + 1) (k – 4)
A. 2k2 – 7k + 4
B. 2k2 –3k + 4
C. 2k2 + 9k + 4
D. 2k2 – 7k – 4
To simplify the expression (2k + 1)(k – 4), we use the distributive property, which states that a(b + c) = ab + ac. Applying this to the expression gives:
(2k + 1)(k – 4) = 2k(k – 4) + 1(k – 4)
Multiplying out the terms within each parentheses gives:
2k(k – 4) = 2k² – 8k
1(k – 4) = k – 4
Putting these back into the original expression and combining like terms gives:
(2k + 1)(k – 4) = 2k² – 8k + k – 4 = 2k² – 7k – 4
Therefore, the answer is D.