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.

   Luz draws the rectangle for (x + 4)(x + 6) 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 + 10x + 24
3. 3.

   Milo draws the rectangle for (x + 2)(x + 7) 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 + 9x + 14
4. 4.

   Ren multiplies (x − 8)(x + 3) and gets x² + ?x − 24. What number goes where the ? is?

   -5
5. 5.

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

   -7
6. 6.

   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
7. 7.

   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
8. 8.

   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
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.

    Milo's photo frame is (4x + 1) cm by (x + 2) cm, with x at least 1. Its perimeter is 2(4x + 1) + 2(x + 2). What is the perimeter in fewest terms?

    10x + 6