1. **State the problem:** Factor the expression $4x^2 - 16$ and draw its graph. 2. **Formula and rules:** To factor expressions like $a^2 - b^2$, use the difference of squares formula: $$a^2 - b^2 = (a - b)(a + b)$$ This applies because both terms are perfect squares. 3. **Apply the formula:** First, recognize that $4x^2 = (2x)^2$ and $16 = 4^2$. So, $$4x^2 - 16 = (2x)^2 - 4^2$$ Using the difference of squares, $$= (2x - 4)(2x + 4)$$ 4. **Simplify factors:** Factor out 2 from each binomial: $$(2x - 4) = 2(x - 2)$$ $$(2x + 4) = 2(x + 2)$$ So, $$(2x - 4)(2x + 4) = 2(x - 2) imes 2(x + 2) = 4(x - 2)(x + 2)$$ 5. **Final factored form:** $$4x^2 - 16 = 4(x - 2)(x + 2)$$ 6. **Graph explanation:** The original expression $y = 4x^2 - 16$ is a parabola opening upwards with vertex at $(0, -16)$. The roots (x-intercepts) are found by setting $y=0$: $$4x^2 - 16 = 0 \Rightarrow x^2 = 4 \Rightarrow x = \pm 2$$ This matches the factors $(x - 2)$ and $(x + 2)$.