Multiply binomials and polynomials, and use them for perimeter and area

Answer Key - Grade 9 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Ren multiplies (3x − 1)(x + 5) with an area model. Type x² as x^2. What is the product in fewest terms?

   3x^2 + 14x - 5
2. 2.

   Tala multiplies (x − 6)(4x + 1) with an area model. Type x² as x^2. What is the product in fewest terms?

   4x^2 - 23x - 6
3. 3.

   Zee multiplies (2x − 5)(3x − 2) with an area model. Type x² as x^2. What is the product in fewest terms?

   6x^2 - 19x + 10
4. 4.

   Bo uses a 2-by-3 area model for (x + 2)(x² − 3x + 4). Type x³ as x^3. What is the product in standard form?

   x^3 - x^2 - 2x + 8
5. 5.

   Esme uses a 2-by-3 area model for (x − 3)(x² + 2x − 1). Type x³ as x^3. What is the product in standard form?

   x^3 - x^2 - 7x + 3
6. 6.

   Jun uses a 2-by-3 area model for (2x + 1)(x² − 4x + 3). Type x³ as x^3. What is the product in standard form?

   2x^3 - 7x^2 + 2x + 3
7. 7.

   Kira uses a 2-by-3 area model for (x − 5)(x² + x + 2). Type x³ as x^3. What is the product in standard form?

   x^3 - 4x^2 - 3x - 10
8. 8.

   Noah's wall painting is (x + 6) feet by (4x − 3) feet, with x at least 1. Type x² as x^2. What is its area in fewest terms?

   4x^2 + 21x - 18
9. 9.

   Tala's door sign is (2x² − 1) inches by (x + 6) inches, with x at least 1. Type x² as x^2. What is its perimeter in fewest terms?

   4x^2 + 2x + 10
10. 10.

    Zee's window is (x² + x) inches by (3x + 4) inches, with x at least 1. Type x² as x^2. What is its perimeter in fewest terms?

    2x^2 + 8x + 8