1. **State the problem:** Expand and simplify the expression $$(x^2+6)(x^2+5)$$. 2. **Formula used:** To expand two binomials, use the distributive property (FOIL method for binomials): $$ (a+b)(c+d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (x^2+6)(x^2+5) = x^2 \cdot x^2 + x^2 \cdot 5 + 6 \cdot x^2 + 6 \cdot 5 $$ 4. **Calculate each term:** $$ x^2 \cdot x^2 = x^{2+2} = x^4 $$ $$ x^2 \cdot 5 = 5x^2 $$ $$ 6 \cdot x^2 = 6x^2 $$ $$ 6 \cdot 5 = 30 $$ 5. **Combine like terms:** $$ x^4 + 5x^2 + 6x^2 + 30 = x^4 + (5x^2 + 6x^2) + 30 = x^4 + 11x^2 + 30 $$ 6. **Final answer:** $$ x^4 + 11x^2 + 30 $$