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

Proved

Step-by-step explanation:

Given

Required

Show that is a multiple of 4

Expand each bracket

Open brackets

Open bracket

Collect Like Terms

Factorize

Hence, the multiples of are and

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the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this