Question

What is a square plus b square?

Answer 1

Hint: Given question is simply based on algebraic identities. We will have to expand or rearrange or modify the identities if needed. First we will convert the word form to variable and algebraic form. And then we will proceed.

Complete step-by-step answer:
Given is, a squared plus b square.
Here a and b are the variables of the identity.
As we know that word form can be written as, \[{a^2} + {b^2}\]
There is no direct formula available for this. So we will transform or modify the already present identities.
We know that, \[{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\]
So in order to find the value of \[{a^2} + {b^2}\] we will take the middle term of the expansion on other side,
\[{\left( {a + b} \right)^2} - 2ab = {a^2} + {b^2}\]
This is the new formula derived from the original identity.
We will try for one more formula, \[{\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}\]
So in order to find the value of \[{a^2} + {b^2}\] we will take the middle term of the expansion on other side,
\[{\left( {a - b} \right)^2} + 2ab = {a^2} + {b^2}\]
This is the new formula derived from the original identity.
Thus we found the value or identity for \[{a^2} + {b^2}\].
So, the correct answer is “\[{\left( {a - b} \right)^2} + 2ab = {a^2} + {b^2}\]”.

Note: Note that both the formulas are very much similar but there is an absolute difference of sign in between.
One uses addition sign and other uses subtraction. This is the only thing to remember while calculating any value based question.