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

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Kira draws the rectangle for (x + 3)(x + 5) and cuts it into four parts, one for each pair of terms. Type x² as x^2. What is the product in fewest terms?

   x^2 + 8x + 15
2. 2.

   Pia multiplies (x + 7)(x − 2) and gets x² + ?x − 14. What number goes where the ? is?

   5
3. 3.

   Zee multiplies (x − 9)(x + 2) and gets x² + ?x − 18. What number goes where the ? is?

   -7
4. 4.

   Ari's rug is (x + 8) by (x + 3) feet (x > 0), so its area is (x + 8)(x + 3). Type x² as x^2. What is the area in fewest terms?

   x^2 + 11x + 24
5. 5.

   Bo's poster is (x + 6) by (x + 3) inches (x > 0), so its area is (x + 6)(x + 3). Type x² as x^2. What is the area in fewest terms?

   x^2 + 9x + 18
6. 6.

   Esme's tabletop is (x + 9) by (x + 4) inches (x > 0), so its area is (x + 9)(x + 4). Type x² as x^2. What is the area in fewest terms?

   x^2 + 13x + 36
7. 7.

   Jun's garden is (x + 7) by (x + 1) feet (x > 0), so its area is (x + 7)(x + 1). Type x² as x^2. What is the area in fewest terms?

   x^2 + 8x + 7
8. 8.

   Kira's photo frame is (2x + 5) cm by (x + 3) cm, with x at least 1. Its perimeter is 2(2x + 5) + 2(x + 3). What is the perimeter in fewest terms?

   6x + 16
9. 9.

   Luz's photo frame is (3x + 2) cm by (x + 6) cm, with x at least 1. Its perimeter is 2(3x + 2) + 2(x + 6). What is the perimeter in fewest terms?

   8x + 16
10. 10.

    Noah's photo frame is (x + 7) cm by (2x + 3) cm, with x at least 1. Its perimeter is 2(x + 7) + 2(2x + 3). What is the perimeter in fewest terms?

    6x + 20