Questions: 16a^2-24a+9

Solution Steps

The given expression \(16a^2 - 24a + 9\) is a quadratic expression. To factor it, we can recognize it as a perfect square trinomial. A perfect square trinomial takes the form \((ax + b)^2 = a^2x^2 + 2abx + b^2\). We need to identify \(a\) and \(b\) such that the expression matches this form.

We start with the quadratic expression given by

\[ 16a^2 - 24a + 9. \]

We can observe that this expression can be factored as a perfect square trinomial. A perfect square trinomial has the form

\[ (ax + b)^2 = a^2x^2 + 2abx + b^2. \]

Upon factoring, we find that

\[ 16a^2 - 24a + 9 = (4a - 3)^2. \]

Final Answer