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.

   Zee works out (5x − 2y)², which has two letters. Type x² as x^2 and y² as y^2. What is (5x − 2y)² in standard form?

   25x^2 - 20xy + 4y^2
3. 3.

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

   9x^2 + 6xy + y^2
4. 4.

   Esme finds 29² without a calculator by writing it as (30 − 1)². What is 29²?

   841
5. 5.

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

   2704
6. 6.

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

   3591
7. 7.

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

   2484
8. 8.

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

   4899
9. 9.

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

   6x + 34
10. 10.

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

    -12x + 40