Question

A, B, and C are polynomials, where A = n, B = 2n + 6, and C = n2 – 1. What is AB – C in simplest form?

Answer 1

B=n2 + 6n + 1

Explanation:

A = n

B = 2n + 6

C = n^2 - 1

AB - C = n * (2n + 6) - (n^2 - 1) = 2n^2 + 6n - n^2 + 1 = n^2 + 6n + 1

Answer 2

The simplest form of the expression AB-C is
`n^2+6n+1`.

Explanation:

In this exercise we only need to use the properties of arithmetic operations and a minimal knowledge of algebraic notation. We have the expressions

• 
  `A = n`,

• 
  `B=2n+6`,

• 
  `C=n^2-1`.

Now we make the indicated operations, beginning by AB:

`AB=n\cdot(2n+6) = 2n^2+6n` using the distributive property of multiplication.

Then, we make AB-C:

`AB-C = 2n^2+6n - (n^2-1) = 2n^2+6n-n^2+1 = n^2+6n+1`.

In the last step we must be vary careful with the change of signs in the expression inside parenthesis.