Question

Which of the equations are true identities?

A. n^3+3n^2+2n=n(n+1)(n+2)
B. (a+3)^2-9=a^2+6a

Answer 1

Both equations A and B are true identities.

For equation A, if we expand the right side of the equation, we get:

n(n+1)(n+2) = n^3 + 3n^2 + 2n

For equation B, if we expand the left side of the equation, we get:

(a+3)^2 - 9 = (a^2 + 6a + 9) - 9 = a^2 + 6a

In both cases, the expanded forms match the original equations, making them true identities.