Verified answer

Step-by-step explanation:

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)

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Step-by-step explanation:

The standard algebraic identities

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)

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