Evaluate the given polynomial using identity
${\left( {b - 7} \right)^2}$

Hint: In this question we should know what are these identities in polynomials. Well, they are basically made to make the question simpler and easier to solve. Like we can observe in this question. The identity used in this question is ${\left( {a - b} \right)^2} = {a^2} + {b^2} - 2ab$ this helps us to answer the question easily. Thus, helping us to use the identities along with the constants which will take long calculations way longer and easy and saving time.

Complete step-by-step answer:

In this question the main concept is the identity, ${\left( {a - b} \right)^2} = {a^2} + {b^2} - 2ab$.

So applying the identity, we get
$
   \Rightarrow {\left( {b - 7} \right)^2} = {b^2} + {\left( 7 \right)^2} - 2.\left( b \right).\left( 7 \right) \\
   \Rightarrow {\left( {b - 7} \right)^2} = {b^2} + 49 - 14b \\
 $
$\therefore $ The expansion of this identity is ${b^2} + 49 - 14b$

Note: Identities are simpler expansions of terms, but we can only use them if they are present in the given form as mentioned.