The document shows the step-by-step multiplication of two polynomials: (57x^8 + 93x^4 - 12x^2)(18x^5 + 79x). It first distributes the terms, then combines like terms to get the final simplified polynomial: 1026x^12 + 6177x^9 - 216x^7 + 7347x^5 - 948x^3.

1. (57x 8 +93x 4 -12x 2 ) (18x 8 +79x 2 )

2. (57x 8 +93x 4 -12x 2 ) (18x 5 +79x) 57x 8 +93x 4 -12x 2 18x 5 79x

3. 57x 8 +93x 4 -12x 2 18x 5 79x ( 57x 8 *18x 5 ) 1026x 12 (93x 4 *18x 5 ) 1674x 9 (-12x 2 *18x 5 ) -216x 7 (57x 8 *79x) 4503x 9 (93x 4 *79x) 7347x 5 (-12x 2 *79x) -948x 3

4. Step 3: Place the product of the numbers in a polynomial equation. (Make sure the numbers are in a DECENDING order by variables.) 57x 8 +93x 4 -12x 2 18x 5 79x 1026x 12 +4503x 9 +1674x 9 -216x 7 +7347x 5 -948x 3 ( 57x 8 *18x 5 ) 1026x 12 (93x 4 *18x 5 ) 1674x 9 (-12x 2 *18x 5 ) -216x 7 (57x 8 *79x) 4503x 9 (93x 4 *79x) 7347x 5 (-12x 2 *79x) -948x 3

5. Step 4: Combine like terms 1026x 12 + 4503x 9 +1674x 9 -216x 7 +7347x 5 -948x 3 1026x 12 +6177x 9 -216x 7 +7347x 5 -948x 3