1. The problem is to identify which trinomials are NOT perfect squares. 2. A perfect square trinomial has the form $$a^2 - 2ab + b^2 = (a - b)^2$$ or $$a^2 + 2ab + b^2 = (a + b)^2$$. 3. We check each trinomial: - For $$x^2 - 4x + 4$$: Compare to $$x^2 - 2\cdot x \cdot 2 + 2^2$$, it matches $$ (x - 2)^2 $$, so it is a perfect square. - For $$x^2 - 10x + 25$$: Compare to $$x^2 - 2\cdot x \cdot 5 + 5^2$$, it matches $$ (x - 5)^2 $$, so it is a perfect square. - For $$x^2 - x + 1$$: Check if $$-x$$ equals $$-2ab$$ for some $$b$$. Here, $$b = \frac{1}{2}$$ would give middle term $$-x$$, but $$b^2 = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \neq 1$$, so it is NOT a perfect square. - For $$x^2 + 6x + 9$$: Compare to $$x^2 + 2\cdot x \cdot 3 + 3^2$$, it matches $$ (x + 3)^2 $$, so it is a perfect square. - For $$x^2 - 8x + 8$$: Check if $$-8x$$ equals $$-2ab$$ for some $$b$$. Here, $$b = 4$$ would give middle term $$-8x$$, but $$b^2 = 16 \neq 8$$, so it is NOT a perfect square. 4. Therefore, the trinomials that are NOT perfect squares are: $$x^2 - x + 1$$ and $$x^2 - 8x + 8$$. Final answer: $$x^2 - x + 1$$ and $$x^2 - 8x + 8$$ are NOT perfect squares.