Squares of binomials and the difference of squares

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Ren works out (2x + 3y)², which has two letters. Type x² as x^2 and y² as y^2. What is (2x + 3y)² in standard form?

   4x^2 + 12xy + 9y^2
2. 2.

   Tala works out (x − 4y)², which has two letters. Type x² as x^2 and y² as y^2. What is (x − 4y)² in standard form?

   x^2 - 8xy + 16y^2
3. 3.

   Bo finds 41² without a calculator by writing it as (40 + 1)². What is 41²?

   1681
4. 4.

   Jun finds 52² without a calculator by writing it as (50 + 2)². What is 52²?

   2704
5. 5.

   Kira finds 57 × 63 without a calculator by writing it as (60 − 3)(60 + 3). What is 57 × 63?

   3591
6. 6.

   Luz finds 46 × 54 without a calculator by writing it as (50 − 4)(50 + 4). What is 46 × 54?

   2484
7. 7.

   Milo finds 69 × 71 without a calculator by writing it as (70 − 1)(70 + 1). What is 69 × 71?

   4899
8. 8.

   Ren simplifies (x − 6)² − (x + 2)(x − 2). Type x² as x^2. What is the result in fewest terms?

   -12x + 40
9. 9.

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

   5x^2 + 12x + 5
10. 10.

    Zee's square rug has side (x + 5) feet. A square mat with side (x + 1) feet lies on it, with x > 0. What area of rug still shows?

    8x + 24