Multiply. Give your answer in standard form.
(2n2 + 5n + 4)(2n – 4)
A. 4n3 – 2n2 + 28n – 16
B. 4n3 + 12n2 – 2n – 16
C. 4n3 + 2n2 – 12n – 16
D. 4n3 + 18n2 – 28n – 16
B. 4n3 + 12n2 – 2n – 16
To multiply the given expression (2n^2 + 5n + 4)(2n - 4), we need to use the distributive property.
First, let's distribute 2n to each term inside the other parentheses:
2n * 2n = 4n^2
2n * -4 = -8n
Next, distribute 5n to each term inside the other parentheses:
5n * 2n = 10n^2
5n * -4 = -20n
Finally, distribute 4 to each term inside the other parentheses:
4 * 2n = 8n
4 * -4 = -16
Now, let's combine like terms:
4n^2 + (-8n) + 10n^2 + (-20n) + 8n + (-16)
Simplifying further:
4n^2 + 10n^2 - 8n - 20n + 8n - 16
Combining like terms again:
(4n^2 + 10n^2) + (-8n - 20n + 8n) - 16
Simplifying:
14n^2 - 20n - 16
So, the correct answer in standard form is:
14n^2 - 20n - 16
Therefore, the correct option is:
D. 14n^2 - 20n - 16