\[\begin{aligned} A &= 9 - x^2& \\ &= 3^2 - x^2& \\ &= (3-x)(3+x).& \end{aligned}\]

\[\begin{aligned} B &= x^2 + 2x + 1& \\ &= x^2 + 2\cdot x \cdot 1 + 1^2& \\ &= (x+1)^2.& \end{aligned}\]

\[\begin{aligned} C &= 4x^2 - 12x + 9& \\ &= (2x)^2 - 2\cdot 2x \cdot 3 + 3^2& \\ &= (2x-3)^2.& \end{aligned}\]

\[\begin{aligned} D &= 9(x+3) + (x+3)^2& \\ &= (x+3)\left[9 + (x+3)\right]& \\ &= (x+3)(9 + x + 3)& \\ & = (x+3)(12 + x).& \end{aligned}\]

\[\begin{aligned} E &= (x-6)^2 - 16& \\ &= (x-6)^2 - 4^2& \\ &= \left[(x-6) - 4\right]\left[(x-6) + 4\right]& \\ &=(x-6-4)(x-6+4)& \\ &= (x-10)(x-2).& \end{aligned}\]

\[\begin{aligned} F &= (2x - 7)^2 - 3(2x - 7)& \\ &= (2x - 7)\left[(2x - 7) - 3\right]& \\ &=(2x-7)(2x - 7 - 3)& \\ &=(2x - 7)(2x - 10).& \end{aligned}\]