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Math Grade 9-12

Polynomial Operations

Adding, subtracting, and multiplying polynomials

View Answer Key

Practice combining like terms and performing operations with polynomials.

Read each problem carefully. Simplify each expression completely and show your work.

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Adding, subtracting, and multiplying polynomials

Math - Grade 9-12

Instructions: Read each problem carefully. Simplify each expression completely and show your work.
  1. 1

    Simplify: (3x^2 + 5x - 7) + (2x^2 - 4x + 9)

  2. 2

    Simplify: (6a^2 - 3a + 8) - (2a^2 + 5a - 1)

  3. 3

    Simplify: 4y(2y^2 - 3y + 5)

  4. 4
    Algebra-tile area model for multiplying two positive binomials.

    Simplify: (x + 7)(x + 3)

  5. 5
    Signed algebra-tile box model showing positive and negative partial products.

    Simplify: (2m - 5)(m + 4)

  6. 6

    Simplify: (5p^2 + 2p - 6) + (3p^2 - 7p + 4)

  7. 7

    Simplify: (7x^3 - 2x^2 + x - 9) - (3x^3 + 4x^2 - 5x + 1)

  8. 8

    Simplify: -3z^2(2z - 5) + 4z

  9. 9
    Signed algebra-tile square model for a binomial squared.

    Simplify: (n - 6)^2

  10. 10
    Signed algebra-tile area model for binomial multiplication with negative partial products.

    Simplify: (3x + 2)(x - 5)

  11. 11

    Simplify: (4r^2 - r + 6) + (2r^2 + 9r - 11) - (r^2 + 3r + 1)

  12. 12

    Simplify: 2t^2(3t^2 - 4t + 7)

  13. 13

    Simplify: (x^2 + 4x + 1) - (2x^2 - x + 8)

  14. 14
    Signed algebra-tile model for a conjugate binomial product.

    Simplify: (2b - 3)(2b + 3)

  15. 15
    Algebra-tile box model for multiplying a linear expression by a quadratic expression.

    Simplify: (x + 2)(x^2 - 3x + 4)

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