Simplify
$$\frac{(x^3+15x^2+75x+125)}{(x^2-25)}(x-5)$$​

Correct option is C

Given:

​$$\frac{(x^3+15x^2+75x+125)}{(x^2-25)}(x-5)$$​​

Formula Used:

​$$(a + b)^2 = a^2 + 2ab + b^2$$​​

​$$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$$​​

Solution:

​$$= \frac{(x^3+15x^2+75x+125)}{(x^2-25)}(x-5)$$​​

​$$=\frac{x^3 + 15x^2 + 75x + 125}{(x - 5)(x + 5)}(x - 5)$$​​

​$$=\frac{x^3 + 15x^2 + 75x + 125}{x + 5}$$​​

​$$=\frac{x^3 + 3(x)(5)(x + 5) + 5^{3}}{x + 5}$$​​

​$$=\frac{(x + 5)^3}{x + 5}$$​​

​$$(x + 5)^2 \\= x^2 + 10x + 25$$​​