Factor perfect squares and the difference of squares

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Jun sorts four cards for a puzzle. Which binomial is a difference of squares?

   • x² − 225
   • x² − 50
   • 6x² − 25
   • x² + 49
2. 2.

   Kira tests four binomials on the board. Which one is a difference of squares?

   • 9x² − 1
   • x² − 20
   • 2x² − 81
   • x² + 100
3. 3.

   Luz finds four binomials in a workbook. Which is a difference of squares?

   • 4x² + 9
   • x² − 169
   • 3x² − 16
   • x² − 27
4. 4.

   Noah cuts a small square out of a big square quilt patch. x² − 36 = (x − ▢)(x + ▢). What number goes in both boxes?

   6
5. 5.

   Pia writes x² − 64 = (x − ▢)(x + ▢) on the board. What number goes in both boxes?

   8
6. 6.

   Ren sees x² − 361 as a square with a square cut out: (x − ▢)(x + ▢). What number goes in both boxes?

   19
7. 7.

   Tala factors x² − 324 = (x − ▢)(x + ▢) for a rug pattern. What number goes in both boxes?

   18
8. 8.

   Zee spots a perfect square: x² + 24x + 144 = (x + ▢)². What number goes in the box?

   12
9. 9.

   Ari builds a square from tiles: x² − 32x + 256 = (x − ▢)². What number goes in the box?

   16
10. 10.

    Esme lays out a square rug pattern: x² + 40x + 400 = (x + ▢)². What number goes in the box?

    20