Factor. \( 16 y^{2}+56 y u+49 u^{2} \) \( \square \)

To factor the expression \( 16 y^{2}+56 y u+49 u^{2} \), notice that it takes the form of a perfect square trinomial. This trinomial can be recognized as \((4y + 7u)^2\) because: 1. The first term \( (4y)^2 = 16y^2 \). 2. The last term \( (7u)^2 = 49u^2 \). 3. The middle term fits the formula \( 2 \times (4y) \times (7u) = 56yu \). So, the factored form is \( (4y + 7u)^2 \). For those curious about the magic behind completing the square and recognizing these patterns, perfect square trinomials are like hidden treasures in math! Keep an eye out for these as you practice; they make factoring so much smoother and quicker! If you ever stumble on similar expressions while studying, remember the structure: \(a^2 + 2ab + b^2\) always factors into \((a + b)^2\). Just identify \(a\) and \(b\) correctly, and you're golden! This can save you tons of time during exams.