Question

$\huge\yellow{What are identities}$​

Answer 1

≈≈> In other words, A = B is an identity if A and B define the same functions, and an identity is an equality between functions that are differently defined. For example, and. are identities. Identities are sometimes indicated by the triple bar symbol ≡ instead of =, the equals sign .

Answer 2

$\huge \tt \underline \orange {Answer}$

In an equation, we use both variables and constants. And here, the value of left hand side(LHS) = right hand side(RHS)An identity is a special equation which holds true for all values of variables.

${ \boxed { \tt \purple { Note :- Here, \: a \: and \: b \: are \: variables }}}$

$\huge \bf\green{Important \: Identities \: are}$

$\bf \pink{(a + b) ^{2} = a ^{2} + 2ab + b ^{2} } \\ \\ \bf \pink{ (a - b) ^{2} = a ^{2} - 2ab + b ^{2} } \\ \\ \bf \pink{ {a}^{2} - {b}^{2} = (a + b)(a - b) } \\ \\ \bf \pink{(x + a)(x - b) = {x}^{2} + x(a + b) + a b } \\ \\\bf \pink{(a + b + c {)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca } \\ \\ \bf \pink{(a + b {)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b)} \\ \\ \bf \pink{(a - b {)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b)} \\ \\ \bf \pink{ {a}^{3} + {b}^{3} + {c}^{3} = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)}$