Question

Factor the expression. 35g^2 – 2gh – 24h^2

Answer 1

Option C: $(7 g-6 h)(5 g+4 h)$ is the correct answer.

Explanation:

The given expression is $35 g^{2}-2 g h-24 h^{2}$

We need to determine the factor of the expression.

Now, let us break the given expression into two groups.

Hence, we get,

$35 g^{2}+28 g h-30 g h-24 h^{2}$

Simplifying, we get,

$\left(35 g^{2}+28 g h\right)+\left(-30 g h-24 h^{2}\right)$

Let us factor out 7g from the term $\left(35 g^{2}+28 g h\right)$

Hence, we have,

$7 g(5 g+4 h)+\left(-30 g h-24 h^{2}\right)$

Similarly, let us factor out -6h from the term $\left(-30 g h-24 h^{2}\right)$

Thus, we have,

$7 g(5 g+4 h)-6 h(5 g+4 h)$

Now, we shall factor out the term $5g+4h$ , we get,

$(7 g-6 h)(5 g+4 h)$

Thus, the factorization of the given expression is $(7 g-6 h)(5 g+4 h)$

Therefore, Option C is the correct answer.