QUESTION 2 2.1) Simplify. 21.1) \( (2 x+3)\left(4 x^{2}-6 x+9\right) \) (3) 2.1.2) \( 2(x-y)^{2}+(x+2 y)(x-2 y) \) 2.2) \( \left(a^{2}-4\right)^{2}-\left(a^{2}+1\right)\left(a^{2}-1\right)+\left(2 a^{2}\right)^{2} \) 22) \( -3 x(3-x)\left(2 x^{2}-x-5\right) \) (2) \( \left(\frac{1}{2} x-3\right)\left(\frac{1}{4} x^{2}+\frac{3}{2} x+9\right) \)

Did you know that polynomial expressions have roots that can often be found using techniques like factoring and the quadratic formula? This is essential when solving equations, as x-values where the polynomial equals zero can be visualized graphically as the points where the curve intersects the x-axis. Remember, every factor corresponds to a unique solution! When simplifying expressions, it's important to watch out for common mistakes like forgetting to distribute or misapplying the distributive property. A fun tip is to always double-check your work by substituting a value for x to see if both the original and simplified expressions yield the same output, ensuring you’ve not only simplified correctly but also preserved the expression's integrity!