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

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Ari multiplies (x³ + 2)(x² − 4x). Type powers like x^5. What is the product in standard form?

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

   Bo multiplies (2x² − 3)(x³ + 5x). Type powers like x^5. What is the product in standard form?

   2x^5 + 7x^3 - 15x
3. 3.

   Esme multiplies (x⁴ − x)(3x² + 2). Type powers like x^5. What is the product in standard form?

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

   Kira simplifies (2x + 1)(x + 3) − (x + 2)(x − 1). Type x² as x^2. What is the result in fewest terms?

   x^2 + 6x + 5
5. 5.

   Luz simplifies (x + 5)(x + 1) − (x − 2)(x + 3). Type x² as x^2. What is the result in fewest terms?

   5x + 11
6. 6.

   Milo simplifies (3x − 1)(x + 2) − (x + 4)(x − 3). Type x² as x^2. What is the result in fewest terms?

   2x^2 + 4x + 10
7. 7.

   Pia pins a (x + 2) by (x + 1) poster on a (x + 6) by (x + 4) board (inches, x ≥ 2). Type x² as x^2. What area is not covered?

   7x + 22
8. 8.

   Zee lays a (x + 2) by (x + 3) rug on a (3x + 2) by (x + 4) floor (feet, x ≥ 2). Type x² as x^2. What area is not covered?

   2x^2 + 9x + 2
9. 9.

   Ari's box is x by (x + 2) by (x + 3) inches, with x at least 2. Type x³ as x^3. What is its volume in standard form?

   x^3 + 5x^2 + 6x
10. 10.

    Bo's box is 2x by (x + 1) by (x + 5) inches, with x at least 2. Type x³ as x^3. What is its volume in standard form?

    2x^3 + 12x^2 + 10x