Question

a^3+3a^2b+3ab^2+b^3怎么变成（a+b)^3

请给我步骤 谢

Answer 1

a^3+3a^2b+3ab^2+b^3=a^3+a^2b+2a^2b+ab^2+2ab^2+b^3

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

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

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

=（a+b)^3

Answer 2

a³ + 3a²b + 3ab² + b³
= (a³ + b³) + (3a²b + 3ab²)
= (a + b)(a² - ab + b²) + 3ab(a + b)
= (a + b)(a² - ab + b² + 3ab)
= (a + b)(a² + 2ab + b²)
= (a + b)³