Which of the following identities is correct?

As we know the standard identities are:

• ${\left(a+b\right)}^2=a^2+2ab+b^2$
• ${\left(a-b\right)}^2=a^2-2ab+b^2$
• $\left(a+b\right)(a-b)=a^2-b^2$

Therefore, ${\left(a+b\right)}^2=a^2+2ab+b^2$ is the correct option.