Mathematical identities

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Across
  1. 2. Number that, when added to a given number, results in zero(15)
  2. 8. The property that states the order of addition or multiplication does not affect the result(10)
  3. 9. The property that states the grouping of numbers for addition or multiplication does not affect the result(9)
  4. 10. The identity that states the product of a sum and a difference is equal to the difference of their squares(10)
Down
  1. 1. Expression for calculating the square of a sum(8)
  2. 3. Distributes multiplication over addition or subtraction(12)
  3. 4. The property that states the distributive property of multiplication over addition(12)
  4. 5. Theorem; In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides(11)
  5. 6. The number that, when multiplied by the original, gives 1 as the product(10)
  6. 7. Equations that are true for all values of the variables involved(8)