To add polynomials in algebra, we group like terms and simplify.

Example 1
(2 x + 5) + (4x + 6)
= (2x + 4x) + (5 + 6) put like terms together inside parentheses
= 6x + 11 simplify

Example 2
(x2 - 6 x - 9) + (- 5 x2 + 9 x + 2)
= (x2 - 5 x2) + (-6 x + 9 x) +(-9 + 2) put like terms together inside parentheses
= - 4 x2 + 3 x - 7 simplify

To subtract polynomials, change signs of all terms of the polynomial preceded by the minus sign and change the subtraction into addition; group like terms and then simplify.

Example 3
(2 x y + x + 5) - (3 x y - 2x + 7)
= (2 x y + x + 5) + (- 3 x y + 2x - 7)
= (2 x y - 3 x y) + (x + 2x) + (7 - 7) = - x y + 3x
Multiple Choice Questions
1. Add the polynomials: (9 x - 6) + (- 5x + 7)
1. 14x + 1
2. -4x - 1
3. 4x + 1
4. 4x + 13
2. Subtract the polynomials: (9 x - 6) - (- 5x + 7)
1. 14x - 13
2. 4x + 1
3. -4x + 13
4. -4x - 13
3. Add the polynomials: (-x2 + 5 x + 2) + (6 x2 + x)
1. 7x2 + 6x + 2
2. 5x2 + 6x + 2
3. 5x2 + 6x
4. 7x2 + 6x
4. Subtract the polynomials: (-x2 + 5 x) - (6 x2 + x - 2)
1. -5x2 + 6x + 2
2. 5x2 + 6x - 2
3. 5x2 + 6x
4. -7x2 + 4x + 2
5. Add the polynomials: (- 7 x2y + xy + 3x + 2) + (5 x2y - 5 xy - 6x - 7)
1. -2x2y - 4 xy - 3x - 5
2. 2x2y + 4 xy - 3x - 5
3. -2x2y - 4 xy + 3x + 5
4. 2x2y + 4 xy + 3x + 5
6. Subtract the polynomials: (- 7 x2y + xy + 3x + 2) - (5 x2y - 5 xy - 6x - 7)
1. - 2x2y - 4 xy - 2x - 5
2. - 12x2y + 6 xy + 9x + 9
3. - 12x2y - 6 xy - 9x - 9
4. 12x2y + 6 xy + 9x + 9
7. Add the polynomials: (xy + 3x + 2) + (3x2 + y)
1. 3x2 + 4 xy + 2
2. 3x2 + 2xy + 3x + 2
3. 3x2 + xy + 3x + y + 2
4. 3x2 + 5 xy + 2
8. Subtract the polynomials: (xy + 3x + 2) - (3x2 + y)
1. 3x2 + 4 xy + 2
2. 3x2 + 4xy + 2
3. -3x2 + 3x - y + 2
4. -3x2 + xy + 3x - y + 2
9. Add the polynomials: (x2y + 3x + 2) + (2 + 2 xy2 + 3x)
1. x2y + 2 xy2 + 6x + 4
2. 3 x2y + 6x + 4
3. 3 xy2 + 6x + 4
4. 3 x2y2 + 6x + 4
10. Subtract the polynomials: (x2y + 3x + 2) - (2 + xy2 + 3x)
1. 0
2. -2 x2y
3. x2y - xy2
4. x2y + xy2

1. C
2. A
3. B
4. D
5. A
6. B
7. C
8. D
9. A
10. C