Algebraic Identities for Class 10

( a + b)2 = a2 + 2ab + b2

( a − b)2 = a2 − 2ab + b2

( a + b)(a – b) = a2 – b2

( x + a)(x + b) = x2 + (a + b)x + ab.

( x + a)(x – b) = x2 + (a – b)x – ab.

( x – a)(x + b) = x2 + (b – a)x – ab.

( x – a)(x – b) = x2 – (a + b)x + ab.

( a + b)3 = a3 + b3 + 3ab(a + b)

Verified answer

Algebraic Identities -:

[tex] \displaystyle \: (a \: + \: b \: ) {}^{2} = {a}^{2} + 2ab + b {}^{2} [/tex]

[tex] \displaystyle \: (a \: - \: b \: ) {}^{2} = {a}^{2} - 2ab + b {}^{2} [/tex]

[tex] \displaystyle(a \: + \: b) \: (a \: - \: b) \: = \: a {}^{2} - {b}^{2} [/tex]

[tex] \displaystyle \: (a + b + c) {}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab \: + 2bc + 2ca[/tex]

[tex](a + b - c) {}^{2} = \: {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc - 2ca[/tex]

Cubes -:

[tex] \displaystyle {a + b}^{ 3} = \: a {}^{3} + {b}^{3} + 3ab \: (a + b)[/tex]