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Adding and subtracting polynomials worksheets Grades 8–9

Combine like terms, changing every sign of a subtracted polynomial.

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Free · Worked example · 21 problems · Answer key · US Letter

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How to do it

Combine like terms. When subtracting, change the sign of every term in the second polynomial.

(3x2+1)+(6x2−5x−2)=(3x2+6x2)+(−5x)+(1−2)=9x2−5x−1(3x^{2} + 1) + (6x^{2} - 5x - 2) = (3x^{2} + 6x^{2}) + (-5x) + (1 - 2) = 9x^{2} - 5x - 1group like terms

Example problems

  1. (x2+6x+5)−(5x2−4x−2)=(x^{2} + 6x + 5) - (5x^{2} - 4x - 2) =
  2. (−6x2−3x−2)+(6x2+6x+3)=(-6x^{2} - 3x - 2) + (6x^{2} + 6x + 3) =
  3. (−3x2−x−5)−(x2+4x+5)=(-3x^{2} - x - 5) - (x^{2} + 4x + 5) =
  4. (x2+3x+5)−(6x2−5x+2)=(x^{2} + 3x + 5) - (6x^{2} - 5x + 2) =

Polynomials and factoring

  1. Exponent rules
  2. Adding and subtracting polynomials
  3. Multiplying a monomial by a polynomial
  4. Multiplying binomials (FOIL)
  5. Special products
  6. Factoring out the GCF
  7. Factoring trinomials
  8. Factoring trinomials with a leading coefficient
  9. Factoring the difference of squares