Question

what is the formula of a cube + b cube​

Answer 1

First method

[math]a^3 + b^3 = a^3 + ab^2 - a^2b + b^3 + a^2b - ab^2 = a(a^2 + b^2 - ab) + b(a^2 + b^2 - ab) = (a + b)(a^2 + b^2 - ab)[/math]

To find [math]a^3 - b^3[/math], replace [math]b[/math] with [math]-[/math][math]b [/math]

[math]a^3 - b^3 = (a - b)(a^2 + b^2 + ab)[/math]

Second method

[math](a + b)^3 = (a + b)^2(a + b) = (a^2 + 2ab + b^2)(a + b) = a^3 + 3a^2b + 3ab^2 + b^3 = a^3 + b^3 + 3ab(a + b) [/math]

[math]a^3 + b^3 = (a + b)^3 - 3ab(a+b) = (a + b)(a^2 + b^2 - ab)[/math]

For [math]a^3 - b^3[/math], replace [math]b[/math] with [math]-b[/math]

[math]a^3 - b^3 = (a - b)^3 + 3ab(a - b) = (a - b)(a^2 + b^2 + ab)[/math]

Answer 2

Answer:

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

Step-by-step explanation:

(a+b)3 - 3ab(a+b)

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