Math, asked by bodomonta871, 9 months ago

show that (a+b)³=a³+b³+3ab(a+b)​

Answers

Answered by umakantjaiswal288
2

Answer:

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

Subtract 3ab(a + b) from each side.

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

Therefore, the formula for (a3 + b3) is

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

Case 2 :

From case 1,

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

a3 + b3 = (a + b)[(a + b)2 - 3ab]

a3 + b3 = (a + b)[a2 + 2ab + b2 - 3ab]

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

Therefore, the formula for (a3 + b3) is

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

So,

(a + b) and (a2 - ab + b2)

are the factors of (a3 + b3).

Similar questions