The expression 9x2 - 100 is equivalent to
1) (9x - 10)(x + 10)
2) (3x - 10)(3x + 10)
3) (3x - 100)(3x - 1)
4) (9x - 100)(x + 1)

2. (3x - 10)(3x + 10)

Step-by-step explanation:

1. (9x - 10)(x + 10)

At first we have to multiply the each part of the expression by the other part of the expression

= (9x*x) + (9x*10) - (10*x) - (10*10)

= 9x^2 + 90x - 10x - 100

After applying adding-deducting rule-

= 9x^2 + 80x - 100

It is not equal to 9x^2 - 100.

2. (3x - 10)(3x + 10)

Again, at first we have to multiply the each part of the expression by the other part of the expression,

= (3x*3x) + (3x*10) - (3x*10) - (10*10)

= 9x^2 + 30x - 30x -100

Since there is a positive 30x and a negative 30x, therefore, both will be eliminated, and we will get,

= 9x^2 - 100

Therefore, it is equal to 9x^2 - 100

3. (3x - 100)(3x - 1)

Again, at first we have to multiply the each part of the expression by the other part of the expression,

= (3x*3x) - (3x*1) - (100*3x) + (100*1) [According to the algebraic rule, (-) x (-) = (+) and (-) x (+) = (-)]

= 9x^2 - 3x - 300x + 100

= 9x^2 - 303x + 100

Therefore, it is not equal to 9x^2 - 100

4. (9x - 100)(x + 1)

Again, at first we have to multiply the each part of the expression by the other part of the expression,

= (9x*x) + (9x*1) - (100*x) - (100*1)

= 9x^2 + 9x - 100x - 100

= 9x^2 - 91x -100

Therefore, it is not equal to 9x^2 - 100.

From the above calculations, we can find that the option 2 [(3x - 10)(3x + 10)] is the correct expression given as question (9x^2 - 100).

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above