Multiplying Polynomial Expressions

Example: Multiply the polynomials, (3x – 5) (4x +2)

Step 1: multiply 3x by 4x = 12x²

Step 2: multiply 3x by 2 = 6x

Step 3: multiply -5 by 4x = -20x

Step 4: multiply -5 by 2 = -10

Step 5: simplify, 12x² + 6x – 12x – 10 = 12x² – 14x – 10

Example: Multiply the polynomials, (2x – 3) (4x² + 2x + 6)

Step 1: multiply 2x by 4x² = 8x³

Step 2: multiply 2x by 2x = 4x²

Step 3: multiply 2x by 6 = 6x

Step 4: multiply -3 by 4x² = -12x²

Step 5: multiply -3 by 2x = -6

Step 6: multiply -3 by 6 = -18

Step 7: simplify, 8x³+ 4x²+ 6x – 12x² – 6x – 18 = 8x³ – 8x² – 18x

Practice Problems

Multiply the following polynomial expressions.

1. (x − 3) (6x − 4)
2. (3y + 6) (2y − 5)
3. (3x − 7) (5x + 3)
4. (2x + 2) (7x² – 3x + 2)
5. (5y− 3) (2y² – 2y + 7)   
6. (6y² – 5y − 6) (3y − 4)
7. (4y² + 6y − 4) (2y − 4)
8. (2p² + 4p – 5) (3p – 2)
9. (8d – 4) (d² + 2d – 3)
10. (3q² – 6q − 4) (2q² + 5q − 5)