n is an integer greater than 1. Prove algebraically that n^2 – 2 – (n – 2)^2 is always an even number.
1) Expand the brackets: (n-2)2 = (n-2)(n-2) = n2 - 2n - 2n +4 = n2 - 4n + 42) Substitute this into the original expression: n2- 2 - (n2 - 4n +4) = n2 - 2 - n2 + 4n - 4 = 4n - 6 3) Reduce this: 4n - 6 = 2(2n - 3)4) Conclusion: This is always an even number as for all values of n the expression is a multiple of 2
JM
Related Maths GCSE answers
All answers ▸We are given a right angled triangle with one side of unknown length. The shortest side is 3cm long, and the longest side is 5cm long. Calculate the remaining side.
Rationalise the denominator of the following fraction: 9/((root13)-1). Write your answer in its simplest form.
Solve the following simultaneous equations: x^2 + 2y = 9, and y = x + 3.
Solve the following definite integral from x=2 to x=-1: ((x^4) + 3(x^2) + 2) dx