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?

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

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

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

   Milo is choosing a binomial to factor at once. Which one is a difference of squares?

   • x² + 36
   • 8x² − 9
   • x² − 72
   • 4x² − 121
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.

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

   19
6. 6.

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

   18
7. 7.

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

   12
8. 8.

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

   16
9. 9.

   Bo checks a square on the board: x² − 28x + 196 = (x − ▢)². What number goes in the box?

   14
10. 10.

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

    20