Question

The product of (n2 – 6n + 3) and -4n is________ When this product is multiplied by -n, the result is________

Answer 1

-4n^3+24n^2-12n, 4n^4-24n^3+12n^2

Answer 2

The product of (n2 – 6n + 3) and -4n is -4n^3+24n^2-12n. When this product is multiplied by -n, the result is 4n^4-24n^3+12n^2.

Explanation:

We have been given an incomplete statement. We are supposed to fill in the blanks for our given statement.

First of all, we will find product of
`(n^2-6n+3)` and
`-4n`.

`-4n(n^2-6n+3)`

Using distributive property
`a(b+c)=ab+ac`, we will get:

`-4n*n^2-4n*-6n-4n*3`

`-4n^3+24n^2-12n`

Therefore, the expression for 1st blank is
`-4n^3+24n^2-12n`.

Now, we will find product of
`(-4n^3+24n^2-12n)` and
`-n`.

`-n(-4n^3+24n^2-12n)`

Using distributive property again
`a(b+c)=ab+ac`, we will get:

`-n*-4n^3-n*24n^2-n*-12n)`

`4n^4-24n^3+12n^2`

Therefore, the expression for 2nd blank is
`4n^4-24n^3+12n^2`.