Question

Expand using algebraic identity: \[{\left( {b - 7} \right)^2}\]

Answer 1

Hint: Here, we have to expand the term by using the algebraic identity. Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In elementary algebra, the symbols representing quantities without having fixed values are known as variables.

Formula used:
We will use the formula of the square of difference of two numbers is given by the algebraic identity \[{\left( {a - b} \right)^2} = {a^2} + {b^2} - 2ab\] where \[a\] and \[b\] are two numbers.

Complete step-by-step answer:
We are given an algebraic expression \[{\left( {b - 7} \right)^2}\].
Now, we have to expand the algebraic expression using an algebraic identity.
Now, substituting \[a = b\] and \[b = 7\] in the algebraic identity \[{\left( {a - b} \right)^2} = {a^2} + {b^2} - 2ab\], we have
\[ \Rightarrow {\left( {b - 7} \right)^2} = {b^2} + {7^2} - 2 \cdot b \cdot 7\]
The square of the variable \[b\] is \[{b^2}\] .
The square of the number \[7\] is \[49\] .
The product of the number and the variable is \[14b\] .
So by substituting the values, we have
\[ \Rightarrow {\left( {b - 7} \right)^2} = {b^2} + 49 - 14b\] .
Therefore, the algebraic expansion of \[{\left( {b - 7} \right)^2}\]is \[{b^2} + 49 - 14b\].

Note: The algebraic equations which are valid for all values of variables in them are called algebraic identities. They are also used for the factorization of polynomials. .
An algebraic expression is an expression which consists of variables and constants. In expressions, a variable can take any value. Thus, the expression value can change if the variable values are changed. But algebraic identity is equality which is true for all the values of the variables.