What is the value of the square of the binomial $a - b$, or what is ${\left( {a - b} \right)^2} = $?
Last updated date: 18th Mar 2023
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Answer
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Hint: Split the expression into two binomials and add the like terms.
In the given problem we need to find the value of the square of the binomial $a - b$ .
${\left( {a - b} \right)^2}{\text{ (1)}}$
Splitting the expression $(1)$ into two binomials, we get
${\left( {a - b} \right)^2} = \left( {a - b} \right) \times \left( {a - b} \right)$
Further multiplying the two binomials, we get
$\left( {a - b} \right) \times \left( {a - b} \right) = {a^2} - ba - ab + {b^2}{\text{ (2)}}$
Since multiplication is a commutative operation,
$ \Rightarrow ab = ba$
Using the above relation in equation $(2)$ and adding the like terms, we get
$\left( {a - b} \right) \times \left( {a - b} \right) = {a^2} - 2ab + {b^2}{\text{ (3)}}$
Form equations $(1)$ and $(3)$ we get
${\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}$ , which is the required answer.
Note: It is advised to remember the above found result as it can be used as an identity to solve the larger polynomial expressions.
In the given problem we need to find the value of the square of the binomial $a - b$ .
${\left( {a - b} \right)^2}{\text{ (1)}}$
Splitting the expression $(1)$ into two binomials, we get
${\left( {a - b} \right)^2} = \left( {a - b} \right) \times \left( {a - b} \right)$
Further multiplying the two binomials, we get
$\left( {a - b} \right) \times \left( {a - b} \right) = {a^2} - ba - ab + {b^2}{\text{ (2)}}$
Since multiplication is a commutative operation,
$ \Rightarrow ab = ba$
Using the above relation in equation $(2)$ and adding the like terms, we get
$\left( {a - b} \right) \times \left( {a - b} \right) = {a^2} - 2ab + {b^2}{\text{ (3)}}$
Form equations $(1)$ and $(3)$ we get
${\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}$ , which is the required answer.
Note: It is advised to remember the above found result as it can be used as an identity to solve the larger polynomial expressions.
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