Factor the following quadratic expression: \( 4 x^{2}+12 x+9 \)

To factor the quadratic expression \( 4x^{2} + 12x + 9 \), notice that it can be rewritten as \( (2x + 3)(2x + 3) \) or \( (2x + 3)^{2} \). This is a perfect square trinomial because if you expand \( (2x + 3)^{2} \), you will get back to the original expression! Another fun fact is that you can also verify your factoring by using the quadratic formula. For \( ax^{2} + bx + c = 0 \), with \( a = 4 \), \( b = 12 \), and \( c = 9 \), the roots can be calculated, and you’ll notice both roots are the same (which confirms it’s a perfect square!). This insight not only deepens your understanding of quadratic functions but also sharpens your algebraic skills!