8. (n + 8)(n + 8) or (n + 8)^2
9. (2x + 1)(2x + 1) or (2x + 1)^2
Step-by-step explanation:
8. n^2 + 16n + 64
What are the factors of 64 that when added will result is 16? It is 8×8.
Therefore,
(n + 8)(n + 8) = (n + 8)^2 = n^2 + 16n + 64
9. 4x^2 + 4x + 1
First, multiply the leading coefficient by constant term. In this case, 4 × 1 = 4
What are the factors of 4 that when added will result in 4? It is 2×2.
Now, replace the middle term with
4x^2 + 2x + 2x + 1.
Now, factor out 4x^2 + 2x and 2x + 1
2x(2x + 1) + 1(2x + 1)
Now factor out 2x + 1
We will be left with
(2x + 1)(2x + 1) = (2x + 1)^2 = 4x^2 + 4x + 1
Hope this helped!
