Factor the polynomial 36a2−84at+49t2

Step 1
Consider the given expression.
${\displaystyle 36a^2-84at+49t^2}$
Step 2
On simplifying the above expression, then
${\displaystyle \Rightarrow {\left(6a\right)}^2-2\times 6a\times 7t+{\left(7t\right)}^2}$
$\Rightarrow (6a{)}^2+(7t{)}^2-2\times 6a\times 7t$
Step 3
Property used:
${\displaystyle {(x-y)}^2=x^2+y^2-2xy}$
Step 4
Therefore, the factor of the given expression will be
${\displaystyle \Rightarrow {(6a-7t)}^2}$
${\displaystyle \Rightarrow (6a-7t)(6a-7t)\dots .[\because {(x-y)}^2=(x-y)(x-y)]}$
Step 5
Answer: The factor of the given expression is equal to (6a-7t)(6a-7t).