If is a constant such that 9x^2+24x^+a is the square of a binomial, then what is a?
Let's turn \(a\) into \(s\), to not get confused with another \(a\). We can see that \(9x^2 + 24x + s = (ax)^2 + abx + abx + b^2\). This equals \((a^2)x^2 + (2ab)x + b^2\). We have that \(9 = (a^2)\), \(24 = (2ab)\), and \(s = b^2\). By \(9 = (a^2)\), \(a = 3\). If \(a = 3\), we can see that \(b = 4\). Then, we can get that \(s = 16\). So your answer would be \(a = 16\).