Shouldn't the final result be 3(-5n+n)(2+n) ?

Question

Why are there supposed to be negative n's?

Answer 1

It would be helpful if you included the original problem for which the final result you are asking about, but since the topic you posted this under is factoring expressions completely then we can find what the original expression should be from the final result you have and work from that.

     3(-5n + n)(2 + n)

Notice that the terms inside the first set of parentheses are like terms and, thus, can be combined:

     (-5n + n) = (-4n)

With this, we have the following:

     3(-5n + n)(2 + n) = 3(-4n)(2 + n)

Distribute -4n among each term inside the second set of parentheses:

     (-4n)(2 + n) = (2(-4n) + n(-4n)) = (-8n - 4n²)

Therefore,

     3(-4n)(2 + n) = 3(-8n - 4n²)

Now, distribute the 3 among each term inside the parentheses:

     3(-8n - 4n²) = (-8n(3) - 4n²(3))

                       = -24n - 12n²

                       = -12n² - 24n

Now we factor this expression completely by finding the greatest common factor (gcf) among the two terms in the expression and factoring it out.

The gcf in this expression is -12n, so factoring -12n out from each term we arrive at the following:

     -12n² - 24n = -12n(n) + -12n(2)

                      = -12n(n + 2)

Answer 2

Now -5n+n=-4n and 3*- 4n=-12n

Therefore the final result can be 3*- 4n*(2+n)=- 12 n (2+n)=-12n(n+2)

To get final answer for sure we need to know the problem.