Verified Answer :

\((6m\pm7)^2=(6m)^2\pm2\cdot6m\cdot7+7^2=\boxed{36m^2\pm84m+49}\\\\Use:(a\pm b)^2=a^2\pm2ab+b^2\)

Answer:

Option a \((6m+ 7)^2=36m^2+49+84m\)

Option d \((6m- 7)^2=36m^2+49-84m\)

Step-by-step explanation:

Given : Expression - \((6m\pm7)^2\)

To find : The square of the given expression

Solution :

We have to solve  \((6m\pm7)^2\)

Apply property : \((a\pm b)^2=a^2+b^2\pm 2ab\)

In the given expression \((6m\pm 7)^2\)

a=6m, b=7

The solution is

\((6m+7)^2=(6m)^2+(7)^2\pm 2(6m)(7)\)

\((6m+7)^2=36m^2+49\pm 84m\)

Therefore,

If the sign is '+' then Option a is correct.

If the sign is '-' then Option d is correct.