The product of the sum and difference of the same two terms is equal to what?

Answer 1

For me, it is equal to the square of the first terms minus the square of the second terms...:-)

For example . . .

(9x + 5) (9x - 5)

= (9x)2 - (5)2

= 81x2 - 25

The former answer was this:

"it is equal to the square of the first term minus the square of the second term"

If we answer in that way, the solution is this:

(9x + 5) - (9x -5)

= (9x + 5)2 - (9x - 5)2

= (81x2 + 25) - (81x2 + 25)

= 81x2 + 25 - 81X2 - 25

= 0

Let us use the DCMC or Dalope's Coefficient Method of Checking: (Checking the answer using only the coefficients)

= (9 + 5) - (9 - 5)

= (14) - (4)

= 10

Our answer to the problem (9x + 5) (9x - 5) using the "it is equal to the square of the first term minus the square of the second term" is 0 but the DCMC answer is 10. There is conflict with the answer!

But if we answer in this way: "it is equal to the square of the first terms minus the square of the second terms" the answer would be 81x2 - 25 and it's answer in DCMC is 56. Let me prove it:

(9 + 5) (9 - 5) (9 + 5) ( 9 - 5)

= (14) (4) or = 81(9 x 9) - 25(5 x -5)

= 56 = 56

Conclusion: The only mistake in the former answer (it is equal to the square of the first term minus the square of the second term) is HIS SOLUTION TO HIS GIVEN EXAMPLE IS CORRECT BUT HIS ANSWER TO THE QUESTION "The product of the sum and difference of the same two terms is equal to what?" IS WRONG OR HE MISSED ONLY TO MAKE THE WORD "TERM" PLURAL!

:-) I hope that my answer will correct your understanding about the above question guys!!!

Jilverex Rain

rex_rain@rocketmail.com