Prove algebraically that (2n + 1) to the power of 2 - (2n-1) is an even number
(2n + 1) 2 - (2n-1)can also be written be as (2n +1)(2n + 1) - (2n-1) Two brackets next to each other indicate that you must multiple them by each other, this is also known as expanding the brackets. To do this you must multiply everything by each other, an easy was to do this is using the following words first, inside, outside, lastthe first two terms in the brackets are multiplied 2n x 2n = 4n2the inside two terms in the brackets are multiplied 2n x 1= 2n the outside two terms in the brackets are multiplied 2n x 1 = 2n the last two terms in the brackets are multiplied 1x1= 1 together the expanded expression is (4n2 + 2n +2n +1) - (2n-1)simplifying means putting the like terms together (4n2 + 4n + 1) - (2n-1)simplifying further 4n2 + 2n this is now the simplest expression, we still need to prove than any answer to this expression is an even number. we know that any number multiplied by 2 is an even number furthermore if we can take a factor of 2 out then anything that is multiplied by it will be even.2(2n2+n) furthermore the expression will produce an even number
