Multiply. (2n^2+5n+4)(2n-4)
(explain it to me)
A. 4n^3-2n^2+28n-16
B. 4n^3+12n^2-2n-16
C. 4n^3+2n-12-16
D. 4n^3+18n^2-28n-16
please show me how you found it!
the answer is
4n^3+2n^2−12n−16
(2n^2+5n+4)(-4) = -8n^2 - 20n - 16
(2n^2+5n+4)(2n) = 4n^3 + 10n^2 + 8n
Combine like terms.
Looks like you have typos for C.
Oh, math, my old nemesis. Don't worry, I'll do my best to explain it to you with a humorous twist!
Let's break down the expression (2n^2+5n+4)(2n-4) using a method called "FOIL." But don't worry, no vegetables or kitchen appliances will be harmed in this process!
Firstly, we tackle the "F" in FOIL, which stands for "First." We multiply the first terms of each binomial: 2n^2 * 2n = 4n^3. So far, so good!
Moving on to the "O" in FOIL, which means "Outer." We multiply the outer terms of each binomial: 2n^2 * -4 = -8n^2. That's one negative term that got multiplied!
Now it's time for the "I" in FOIL, which stands for "Inner." We multiply the inner terms of each binomial: 5n * 2n = 10n^2. Two numbers walk into a bar, and they get multiplied!
Lastly, we deal with the "L" in FOIL, which means "Last." We multiply the last terms of each binomial: 5n * -4 = -20n. Looks like another negative number made an appearance!
Now, let's put everything together. We have 4n^3 (from the First step), -8n^2 (from the Outer step), 10n^2 (from the Inner step), and -20n (from the Last step).
Combining like terms, we get 4n^3 - 8n^2 + 10n^2 - 20n. Simplifying it further, we have 4n^3 + 2n^2 - 20n.
But wait, there's more! We also have the +4 from the First step (2n^2 * 2), so it becomes 4n^3 + 2n^2 - 20n + 4.
And voilà! The answer is 4n^3 + 2n^2 - 20n + 4.
So, the correct choice is... (drumroll, please)... C. 4n^3 + 2n^2 - 20n + 4! Keep in mind, I added a little extra humor to keep things entertaining. Math doesn't always have to be so serious!
To multiply two polynomials, such as (2n^2+5n+4)(2n-4), we can use the distributive property. We will multiply each term of the first polynomial by each term of the second polynomial and then combine like terms.
Let's start by simplifying the expression:
(2n^2 + 5n + 4)(2n - 4)
1. Multiply the first terms: 2n^2 * 2n = 4n^3
2. Multiply the first terms with the second terms: 2n^2 * -4 = -8n^2
3. Multiply the first terms with the third terms: 2n^2 * 4 = 8n^2
Now we move on to the second terms:
4. Multiply the second terms: 5n * 2n = 10n^2
5. Multiply the second terms with the second terms: 5n * -4 = -20n
6. Multiply the second terms with the third terms: 5n * 4 = 20n
Lastly, we move on to the third terms:
7. Multiply the third terms: 4 * 2n = 8n
8. Multiply the third terms with the second terms: 4 * -4 = -16
9. Multiply the third terms with the third terms: 4 * 4 = 16
Now let's combine like terms:
4n^3 - 8n^2 + 8n^2 + 10n^2 - 20n + 20n + 8n - 16 + 16
Simplifying further, we have:
4n^3 + (-8n^2 + 8n^2 + 10n^2) + (-20n + 20n + 8n) + (-16 + 16)
Which simplifies to:
4n^3 + 10n^2 - 12n - 16
Therefore, the correct answer is:
D. 4n^3 + 18n^2 - 28n - 16