Question

Give some Algebraic Identities.​

Answer 1

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Give some Algebraic Identities.

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(i) (a+b)(a-b) = a²-b²

(ii) (a+b)² = a²+2ab+b² = (a-b)²+4ab

(iii) (a-b)² = a²-2ab+b² =(a²+b²+2ab)-4ab= (a+b)²-4ab

(iv) (a²-b²) = (a-b)(a+b)

(v) (a+b)³ = a³+b³+3a²b+3ab² = a³+b³+3ab(a+b)

(vi) (a-b)³ = a³-b³-3a²b+3ab² = a³-b³-3ab(a-b)

(vii) a³+b³ = (a+b)(a²+b²-ab) = (a+b)³-3ab(a+b)

(viii)a³-b³ = (a-b) (a²+b²+ab) = (a-b)³-3ab(a+b)

(ix) (a+b+c)² = a²+b²+c²+2ab+2bc+2ca = a²+b²+c²+2(ab+bc+ac)

(x) a²+b²+c² = (a+b+c)²-2(ab+bc+ac)

(xi) (a+b+c)³ = a³+b³+c³+3(a+b)(b+c)(c+a)

(xii) a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-ab-bc-ac)

Answer 2

Some Standard Algebraic Identities list are given below:

Identity I: (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)