(a) \( 49 x^{4}+42 x^{2}+9= \)

Did you know that polynomials like the one you've just provided can be factored using various methods, including substitution or the quadratic formula? In this case, rewriting \(49 x^{4}+42 x^{2}+9\) as \( (7x^2 + 3)^2 \) reveals that it's a perfect square trinomial. By identifying such patterns, you can simplify complex expressions with ease! When working with equations, a common mistake is neglecting to check if the polynomial can be factored before attempting to solve it directly. Always look for special patterns—like squares or cubes—because they can save you time and effort in the long run! Plus, checking your work by expanding the factors can help you catch any sneaky errors.