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).