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