1. **State the problem:** Factor the quadratic expressions and match them with their correct factored forms. 2. **Recall factoring formulas:** - Difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$ - Perfect square trinomial: $$a^2 \pm 2ab + b^2 = (a \pm b)^2$$ 3. **Factor each expression:** - For $$x^2 - 16$$: This is a difference of squares with $$a = x$$ and $$b = 4$$. So, $$x^2 - 16 = (x - 4)(x + 4)$$. - For $$x^2 + 8x + 16$$: Check if it is a perfect square trinomial. $$8x = 2 \times x \times 4$$ and $$16 = 4^2$$, so yes. Therefore, $$x^2 + 8x + 16 = (x + 4)^2$$. - For $$x^2 + 10x + 16$$: Try to factor as $$(x + m)(x + n)$$ where $$m + n = 10$$ and $$mn = 16$$. Factors of 16 are (1,16), (2,8), (4,4). None sum to 10, so it does not factor nicely over integers. 4. **Match answers:** - $$x^2 - 16$$ matches with $$(x + 4)(x - 4)$$. - $$x^2 + 8x + 16$$ matches with $$(x + 4)^2$$. - $$x^2 + 10x + 16$$ does not match any given factorization options. **Final answers:** - $$x^2 - 16 = (x + 4)(x - 4)$$ - $$x^2 + 8x + 16 = (x + 4)^2$$ - $$x^2 + 10x + 16$$ has no integer factorization from the given options.