Question

write the formula of (a+b)³ ?

Answer 1

Answer:

The formula of $(a+b)^{3}$ is a³-3a²b+3ab²-b³.

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Answer 2

The formula of (a+b)³=  (a+b)^3=a^3 + 3ab (a + b) + b^3

Derivation of formula.

(a + b)^3 can be written as,

(a + b) * (a + b) * (a + b)

Let's multiply the first two terms.

[ (a +b) * (a + b) ] * (a + b)

[ a*a + a*b + b*a + b*b] * (a + b)

(a^2 + ab + ab + b^2) * (a + b)

(a^2 + 2ab + b^2) * (a + b)

Let's proceed further and multiply the terms in two parentheses.

=> ( a^2 * a + a^2 * b +2ab * a + 2ab * b +b^2 * a + b^2 * b )

=> (a^3 + ba^2 + 2ba^2 + 2ab^2 + ab^2 + b^3)

=> (a^3 + 3ba^2 + 3ab^2 + b^3)

We can rewrite this formula further.

=>[a^3 + 3ab (a + b) + b^3]

Therefore, (a + b)^3 = a^3 + 3ab (a + b) + b^3