Answer:
A. III only
Step-by-step explanation:
In mathematics, an identity is one of the characteristics of algebraic expressions.
Given variable a and b in an algebraic expression, an identity is defined as an equality that remains the same no matter the values that we choose for either variable a or b.
Identity in mathematics makes it very easy to solve algebraic expressions. The two sides of an identity in an algebra can easily be exchanged for each other.
In the above question, we are given 3 Options.
I) 3(5 + 2x) = 15 + 6x
II) y = x + 3
III) (x² - y²) = (x + y) (x - y)
Option I) 3(5 + 2x) = 15 + 6x
Is showing distributive property in mathematics.
Distributive property is :
a(b + c) = ab + ac
Option I is not an identity , therefore it is wrong.
Option II) y = x + 3 is just an algebraic expression.
Only Option III is an identity. This is because it follows the rule of
(a² - b²) = (a + b) (a - b)
We can prove and confirm this be solving the algebraic expression
(x + y) (x - y)
We expand the bracket
x² - xy +xy - y²
x² - y²
Therefore, option A is the correct option.
→ 
→ 
![\sqrt{[(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}]}](https://tex.z-dn.net/?f=%5Csqrt%7B%5B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%5D%7D%20)
![\sqrt{[(3-(-4))^{2}+(-1-(-5))^{2}]}](https://tex.z-dn.net/?f=%5Csqrt%7B%5B%283-%28-4%29%29%5E%7B2%7D%2B%28-1-%28-5%29%29%5E%7B2%7D%5D%7D%20)
![\sqrt{[7^{2}+4^{2}]}](https://tex.z-dn.net/?f=%5Csqrt%7B%5B7%5E%7B2%7D%2B4%5E%7B2%7D%5D%7D%20)
![\sqrt{[49+16]}](https://tex.z-dn.net/?f=%5Csqrt%7B%5B49%2B16%5D%7D%20)
