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

Question

Mathematics

Isabel Barton

7 January, 07:24

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

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Answers (1)

Know the Answer?

Jaida Carr · Answer 1

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