(2n+1)(2n-1)(n+5)
I'm a little confused on how to do this one.
Any help would be greatly appreciated!!!
Thanks.
see the other post.
see the other post.
Hi Chelsea:
You are given three binomials which are to be multiplied. Were you asked to multiply three numbers, e.g., (3)(4)(7), you would likely multiply any two, and then combine the result with the third number for the final product. Well, the overall strategy is the same for three binomials. Beginning with(2n+1)(2n-1), we recognize them as being a conjugal pair, the product of which is the difference of two squares. That is,
(2n+1)(2n-1) = (2n)^2 - (1)^2 = 4n^2 - 1.
Finally, use FOIL to evaluate
(4n^2 - 1)(n - 5) and you are done. I leave the details for you to complete.
Regards,
Rich B.
Correction: The third binomial is given as (n+5), as opposed to (n-5) as I have in the previous post.
Rich B.
Just use the foil method.
F irst
O utside
I nside
L ast
Mult. the first set of () together then the product of that to the last () and you'll have the answer.
To multiply the expression (2n+1)(2n-1)(n+5), we can use the FOIL method.
1. Multiply the first two binomials (2n+1)(2n-1) using the difference of squares formula:
(2n+1)(2n-1) = (4n^2 - 1)
2. Now multiply the result (4n^2 - 1) with the third binomial (n+5):
(4n^2 - 1)(n+5) = 4n^2(n) + 4n^2(5) - 1(n) - 1(5)
= 4n^3 + 20n^2 - n - 5
So, the final product is 4n^3 + 20n^2 - n - 5.
To multiply the expression (2n+1)(2n-1)(n+5), you can use the distributive property and the FOIL method. Here's the step-by-step explanation:
Step 1: Multiply the first two binomials, (2n+1)(2n-1), using the difference of squares formula. This formula states that (a+b)(a-b) = a^2 - b^2, where a and b can be any expressions. In this case, a = 2n and b = 1.
(2n+1)(2n-1) = (2n)^2 - (1)^2
= 4n^2 - 1
Step 2: Now multiply the result from step 1, 4n^2 - 1, with the third binomial, (n+5), using the FOIL method. The FOIL method stands for First, Outside, Inside, Last and is used to multiply two binomials. Multiply each pair of terms and combine like terms in the end.
(4n^2 - 1)(n+5) = 4n^2 * n + 4n^2 * 5 - 1 * n - 1 * 5
= 4n^3 + 20n^2 - n - 5
So, the expression (2n+1)(2n-1)(n+5) simplifies to 4n^3 + 20n^2 - n - 5.