1. **State the problem:** Simplify the expression $$ (112128.28-60x^2)(46135.98-28.03x^2) - (-46135.98)^2 $$. 2. **Recall the formula:** We will expand the product of two binomials and then subtract the square of a number. 3. **Expand the product:** $$ (112128.28)(46135.98) - (112128.28)(28.03x^2) - (60x^2)(46135.98) + (60x^2)(28.03x^2) $$ 4. **Calculate each term:** $$ 112128.28 \times 46135.98 = 5174049999.9944 $$ $$ 112128.28 \times 28.03x^2 = 3140952.4484x^2 $$ $$ 60x^2 \times 46135.98 = 2768158.8x^2 $$ $$ 60x^2 \times 28.03x^2 = 1681.8x^4 $$ 5. **Rewrite the expanded expression:** $$ 5174049999.9944 - 3140952.4484x^2 - 2768158.8x^2 + 1681.8x^4 $$ 6. **Combine like terms:** $$ 5174049999.9944 - (3140952.4484 + 2768158.8)x^2 + 1681.8x^4 $$ $$ = 5174049999.9944 - 5909111.2484x^2 + 1681.8x^4 $$ 7. **Calculate the square:** $$ (-46135.98)^2 = 2128469999.3604 $$ 8. **Subtract the square:** $$ 5174049999.9944 - 5909111.2484x^2 + 1681.8x^4 - 2128469999.3604 $$ 9. **Simplify constants:** $$ (5174049999.9944 - 2128469999.3604) - 5909111.2484x^2 + 1681.8x^4 $$ $$ = 3045580000.634 - 5909111.2484x^2 + 1681.8x^4 $$ **Final simplified expression:** $$ 3045580000.634 - 5909111.2484x^2 + 1681.8x^4 $$