Prove: The square of a number that is one more than a multiple of 3 is also one more than a multiple of 3

  3(3n² +2n) +1

Step-by-step explanation:

All you have to do is factor the greatest common (integer) factor from the two terms containing n

The greatest common factor of 3·3 = 9 and 3·2 = 6 is 3. That's what goes in the green box outside parentheses. Then the numbers inside parentheses are the remaining factors of those coefficients:

  3(3n² +2n) +1

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The fact that you're concerned with multiples of 3 is an additional clue that 3 is a factor of the product. So, the form you're looking for is 3( ) +1.