### Instruction: If $a$ is a constant such that $9x^2 + 24x + a$ is the square of a binomial, then what is $a$?### Response: I need to find a value of $a$ that makes $9x^2 + 24x + a$ a perfect square trinomial.
That means it should have the form $(3x + b)^2$, where $b$ is some constant.
Expanding $(3x + b)^2$, I get $9x^2 + 6bx + b^2$.
Comparing this to $9x^2 + 24x + a$, I see that $6bx = 24x$, so $b = 4$.
Then, $b^2 = 16$, so $a = 16$.
To check, I can factor $9x^2 + 24x + 16$ as $(3x + 4)^2$, which confirms that it is a perfect square.