Question

Tell me all useful algebraic identities..

Answer 1

Answer:

Some Standard Algebraic Identities list are given below:

Identity I: (a + b)2 = a2 + 2ab + b2

Identity II: (a – b)2 = a2 – 2ab + b2

Identity III: a2 – b2= (a + b)(a – b)

Identity IV: (x + a)(x + b) = x2 + (a + b) x + ab

Identity V: (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

Identity VI: (a + b)3 = a3 + b3 + 3ab (a + b)

Identity VII: (a – b)3 = a3 – b3 – 3ab (a – b)

Identity VIII: a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)

Step-by-step explanation:

Answer 2

$\boxed{ \boxed{ \overline{ \underline{ \bf \red{USEFUL \: ALGEBRAIC \: IDENTITIES ☻}}}}}$

$\rm \: The \: algebraic \: identities \: given \: below \: will \: help \: you \: in \:$

$\rm \: factorising \: the \: polynomials : -$

$\rm \: i) \: (a ± b) {}^{2} = a {}^{2} + b {}^{2}± 2ab$

$\rm \: ii) \: (a + b) {}^{2} - (a - b) {}^{2} = 4ab$

$\rm \: iii) \: (a {}^{2} - b {}^{2} ) = (a + b)(a - b)$

$\rm \: iv) \: (a {}^{3} ± b {}^{3} ) = (a±b)(a {}^{2} + b {}^{2} ± ab)$

$\rm \: v) \: (a + b + c) {}^{2} = a {}^{2} + b {}^{2} + c {}^{2} + 2(ab + bc + ac)$

$\rm \: vi) \: (a + b) {}^{3} = a {}^{3} + b {}^{3} + 3ab(a + b) \: or \: a {}^{3} + b {}^{3} + 3a {}^{2} b + 3ab {}^{2}$

$\rm \: vii) \: (a - b) {}^{3} = a {}^{3} - b {}^{3} - 3ab(a - b) \: or \: a {}^{3} - b {}^{3} - 3a {}^{2} b + 3ab {}^{2}$

$\rm \: viii) \: a {}^{3} + b {}^{3} + c {}^{3} - 3abc = (a + b + c)(a {}^{2} + b {}^{2} + c {}^{2} - ab - bc - ca)$