Question

If a+b=-1 then a^3+b^3-3ab

Answer 1

Answer:

-1

Step-by-step explanation:

1. Identity

• $(A+B)^3=A^3+3A^2B+3AB^2+B^3$
• $A^3+3A^2B+3AB^2+B^3=A^3+B^3+3AB(A+B)$

2. Substitute $A=a$ and $B=b$ into the identity.

• $(a+b)^3=a^3+3a^2b+3ab^2+b^3$
• $a^3+3a^2b+3ab^2+b^3=a^3+b^3+3ab\times (-1)$

$(a+b)^3=a^3+b^3-3ab$

∴ $-1$