To multiply the polynomials 2x+y and 5x-y+3 using a table, we can follow these steps:
Write the two polynomials side by side, with the terms arranged in descending order of degree:
2x + y
x | 5x - y + 3
Multiply each term in the first polynomial by each term in the second polynomial, and write the products in the table:
2x y
x | 5x² -xy 3x
-y y² -3y
5x² -xy +3x
-y² +3y
Simplify the products by combining like terms:
5x² -xy +3x -y² +3y
Therefore, the product of the polynomials 2x+y and 5x-y+3 is 5x² -xy +3x -y² +3y.