b. \( \quad 16 b^{2}+50 b c^{2}+25 c^{4} \)

Did you know that the expression \( 16b^{2} + 50bc^{2} + 25c^{4} \) can be factored? If you observe closely, you'll notice that this is a perfect square trinomial! It can be rewritten as \( (4b + 5c^{2})^{2} \). Recognizing patterns like this is a key skill in algebra that can make simplifying expressions much easier. When tackling polynomials, one common mistake is to overlook the possibility of factoring. Always check for perfect squares and common factors before diving into more complex operations. Another helpful tip? Sketch out a few terms or values to visualize how the polynomial might behave—this can often deepen your understanding and help you spot potential factorizations or simplifications!