Question

Give me all algebraic identities which we have studied from 5th to 9th and using in 10th.

Answer 1

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)

Answer 2

(a+b)² = a²+b²+2ab

(a+b+c)² = a²+b²+ c²+2(ab+bc+ac)

(a-b)² = a²+ b² -2ab

(a-b)³ = a³-b³+3ab²-3a²b

(a+b)³ = a³+b³+3ab²+3a²b

(a+b)(a-b) = a²-b²

a³+b³= (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)
Hope it helps☺️