Option C:
is the correct answer.
Explanation:
The given expression is ![35 g^{2}-2 g h-24 h^{2}](https://tex.z-dn.net/?f=35%20g%5E%7B2%7D-2%20g%20h-24%20h%5E%7B2%7D)
We need to determine the factor of the expression.
Now, let us break the given expression into two groups.
Hence, we get,
![35 g^{2}+28 g h-30 g h-24 h^{2}](https://tex.z-dn.net/?f=35%20g%5E%7B2%7D%2B28%20g%20h-30%20g%20h-24%20h%5E%7B2%7D)
Simplifying, we get,
![\left(35 g^{2}+28 g h\right)+\left(-30 g h-24 h^{2}\right)](https://tex.z-dn.net/?f=%5Cleft%2835%20g%5E%7B2%7D%2B28%20g%20h%5Cright%29%2B%5Cleft%28-30%20g%20h-24%20h%5E%7B2%7D%5Cright%29)
Let us factor out 7g from the term ![\left(35 g^{2}+28 g h\right)](https://tex.z-dn.net/?f=%5Cleft%2835%20g%5E%7B2%7D%2B28%20g%20h%5Cright%29)
Hence, we have,
![7 g(5 g+4 h)+\left(-30 g h-24 h^{2}\right)](https://tex.z-dn.net/?f=7%20g%285%20g%2B4%20h%29%2B%5Cleft%28-30%20g%20h-24%20h%5E%7B2%7D%5Cright%29)
Similarly, let us factor out -6h from the term ![\left(-30 g h-24 h^{2}\right)](https://tex.z-dn.net/?f=%5Cleft%28-30%20g%20h-24%20h%5E%7B2%7D%5Cright%29)
Thus, we have,
![7 g(5 g+4 h)-6 h(5 g+4 h)](https://tex.z-dn.net/?f=7%20g%285%20g%2B4%20h%29-6%20h%285%20g%2B4%20h%29)
Now, we shall factor out the term
, we get,
![(7 g-6 h)(5 g+4 h)](https://tex.z-dn.net/?f=%287%20g-6%20h%29%285%20g%2B4%20h%29)
Thus, the factorization of the given expression is ![(7 g-6 h)(5 g+4 h)](https://tex.z-dn.net/?f=%287%20g-6%20h%29%285%20g%2B4%20h%29)
Therefore, Option C is the correct answer.