1. **State the problem:** Factor the polynomial $$4x + 16 + xy + 4y$$ by grouping. 2. **Group terms:** Group the polynomial into two pairs: $$ (4x + 16) + (xy + 4y) $$ 3. **Factor each group:** - From $$4x + 16$$, factor out $$4$$: $$4(x + 4)$$ - From $$xy + 4y$$, factor out $$y$$: $$y(x + 4)$$ 4. **Factor out the common binomial:** Both groups contain $$ (x + 4) $$, so factor it out: $$ (x + 4)(4 + y) $$ 5. **Final factored form:** $$ (x + 4)(y + 4) $$ **Explanation:** We used factoring by grouping, which involves grouping terms to find common factors. Here, grouping the first two and last two terms allowed us to factor out common binomials, resulting in the product of two binomials. **Answer:** $$4x + 16 + xy + 4y = (x + 4)(y + 4)$$