Answer: The correct option is
(C) \((10x-7)(10x+7).\)
Step-by-step explanation: We are given to factor completely the following quadratic expression :
\(E=100x^2-49~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We will be using the following factorization formula :
\(a^2-b^2=(a-b)(a+b).\)
The factorization of expression (i) is as follows :
\(E\\\\=100x^2-49\\\\=(10x)^2-7^2\\\\=(10x-7)(10x+7).\)
Thus, the required factored form of the given expression is \((10x-7)(10x+7).\)
Option (C) is CORRECT.
