Mathematics: Prove that (n+5)^2-(n+3)^2 is a multiple of 4 for all positive integer values of n

Prove that (n+5)^2-(n+3)^2 is a multiple of 4 for - id5232410386905, ddaaaeeee2960

isabelperez063

17.03.2022

Proved

Step-by-step explanation:

Given

(n+5)^2-(n+3)^2

Required

Show that (n+5)^2-(n+3)^2 is a multiple of 4

Expand each bracket

(n+5)(n+5)-(n+3)(n+3)

Open brackets

n^2 + 5x + 5x + 25 - (n^2 + 3x + 3x + 9)

n^2 + 10x + 25 - (n^2 + 6x + 9)

Open bracket

n^2 + 10x + 25 - n^2 - 6x - 9

Collect Like Terms

- n^2 + n^2 - 6n + 10n + 25 - 9

- 6n + 10n + 25 - 9

4n + 25 - 9

4n + 16

Factorize

4(n + 4)

Hence, the multiples of (n+5)^2-(n+3)^2 are and (n + 4)

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jerry7792

02.03.2021

Step-by-step explanation:

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