Question

Prove that for any natural n the value of the expression (4n+5)^2–9 is divisible by 4.

thank you !!!
please show work, not just the answer

Answer 1

4 n (2) + 10 n +4

Explanation:

Answer 2

Explanation:

Simplify the expression by opening parenthesis:

• (4n + 5)² - 9 =
• (4n)² + 2*5*(4n) + 25 - 9 =
• 4(4n²) + 4(10n) + 4(4) =
• 4(4n² + 10n + 4)

As we see the expression has 4 as one of factors so is divisible by 4.