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.

   Pia multiplies (2x + 3)(x − 4) with an area model. Type x² as x^2. What is the product in fewest terms?

   2x^2 - 5x - 12
2. 2.

   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
3. 3.

   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
4. 4.

   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
5. 5.

   Luz's vegetable garden is (3x − 2) meters by (x + 4) meters, with x at least 1. Type x² as x^2. What is its area in fewest terms?

   3x^2 + 10x - 8
6. 6.

   Milo's patio is (2x + 5) feet by (2x − 1) feet, with x at least 1. Type x² as x^2. What is its area in fewest terms?

   4x^2 + 8x - 5
7. 7.

   Pia's quilt is (5x − 4) feet by (x + 2) feet, with x at least 1. Type x² as x^2. What is its area in fewest terms?

   5x^2 + 6x - 8
8. 8.

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

   2x^2 + 4x + 8
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