If $a^3 +3a^2 + 3a = 63,$ then the value of $a^2 +2a$ is :

15

Let's solve the given equation a³+3a²+3a=63 and find the value of a²+2a

We can factor the left side of the equation by recognizing it as a cube of a binomial:

(a+1)³=a³+3a²+3a+1

Comparing this with the given equation, we have:

(a+1)³=63+1

Taking the cube root of both sides, we get:

a + 1 = ∛(64)

Simplifying further, we have:

a + 1 = 4

Subtracting 1 from both sides:

a = 4 - 1

a = 3

Now we can find the value of $a^2 +2a$ = $3^2 +2×3$ = 15