Adding and subtracting polynomial expressions

To add or subtract polynomials first use the commutative property to group like terms then use the distributive property to add or subtract them.

Example: Add the polynomial expressions, (2x + 3y) + (4x + 2y)

We add as we normally do in arithmetic.   

Example: Add the polynomial expressions, (3x² + 5x + 2) + (2x² + 3x + 6)

Again, we add as in arithmetic

Example: Subtract the polynomial expressions, (6x²+ 7x + 8) – (2x²+ 3x + 4)

Since we are subtracting all the signs in the second parenthesis change to the opposite sign.

Example: Subtract the polynomial expressions, (5x² + 6y² – 2x + 3y + 4) – (2x²– 4y² +2x + y – 3)

Again, all the signs in the second parenthesis change to the opposite sign.

Practice Problems

Add or subtract the following polynomial expressions.

1. (5x² + 3x – 4) + (4x² – x – 2)
2. (2x³ + 4x² – 3x – 5) + (3x² + 6x + 7)
3. (6x³ – 4x² + x – 9) – (2x²+ 3x + 4)
4. (5y² – 3y + 8) – (2y² + 3y + 4)
5. (2x + 4xy + 3y) + (3x – 2xy + 5y)
6. (x²y + 3xy² – 2x + 3y) + (4xy² + 5x + 2y)
7. (4x²y² – 3xy + 2x – 4y) – (-2x²y² + 5xy + 6x – 9y)
8. (8x³ + 5x² – 2x – 5) + (-3x³ – 2x² + 7x + 2)
9. (12y⁴ + 8y³ + 5y² – 6y – 3) – (7y⁴ – 2y³ + 6y² – 2y + 4)
10. (10x² – 3x²y² + 6xy – x – y) – (5x² – 2x²y² – 2xy + 3x + 5y)