If a+b=1, find N=a^3+b^3+3ab

Answer: 1

Step-by-step explanation:

a + b = 1

a³ + b³ = (a + b) (a² - ab + b²) formula for a perfect cube

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

↓

= 1 (a² - ab + b²) + 3ab

= a² - ab + b² + 3ab

= a² + 2ab + b² this is a perfect square

= (a + b) (a + b)

↓ ↓

= (1) (1)

= 1

1

Step-by-step explanation:

Using the identity

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

a³ + b³ + 3ab (a + b) = (a + b) ³

a³ + b³ + 3ab (1) = 1³, hence

a³ + b³ + 3ab = 1