1. **State the problem:** Multiply the expressions $$(7x^2 + a^2)(x^2 - 3a^2)$$. 2. **Recall the distributive property:** To multiply two binomials, multiply each term in the first binomial by each term in the second binomial. 3. **Apply the distributive property:** $$7x^2 \cdot x^2 + 7x^2 \cdot (-3a^2) + a^2 \cdot x^2 + a^2 \cdot (-3a^2)$$ 4. **Calculate each term:** $$7x^2 \cdot x^2 = 7x^{2+2} = 7x^4$$ $$7x^2 \cdot (-3a^2) = -21a^2x^2$$ $$a^2 \cdot x^2 = a^2x^2$$ $$a^2 \cdot (-3a^2) = -3a^{2+2} = -3a^4$$ 5. **Combine all terms:** $$7x^4 - 21a^2x^2 + a^2x^2 - 3a^4$$ 6. **Simplify like terms:** $$-21a^2x^2 + a^2x^2 = (-21 + 1)a^2x^2 = -20a^2x^2$$ 7. **Final expression:** $$7x^4 - 20a^2x^2 - 3a^4$$ This is the product of the two binomials.