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.

   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
6. 6.

   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
7. 7.

   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
8. 8.

   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
9. 9.

   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
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