Given that n is an integer and that n>1, prove algebraically that n²-(n-2)²-2 is always an even number

Mathematics

1 answer:

photoshop1234 [79]2 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

Any integer n > 1 multiplied by 2 will be even, that is

2n ← is even

Given

n² - (n - 2)² - 2 ← expand parenthesis

= n² - (n² - 4n + 4) - 2

= n² - n² + 4n - 4 - 2 ← collect like terms

= 4n - 6 ← factor out 2 from each term

= 2(2n - 3)

Hence 2(2n - 3) ← will always be even for n > 1

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