Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Algebra 1

9.1.5 Practice

Algebra 19.1.5 Practice
Search for key terms or text.

9.1.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

  1. Select three expressions that are perfect squares.
  1. ( x + 5 ) ( x + 5 )
  2. ( − 9 + c ) ( c − 9 )
  3. ( y − 10 ) ( 10 − y )
  4. ( 2 x − 1 ) ( 2 x + 1 )
  5. ( 4 − 3 x ) ( 3 − 4 x )
  6. ( a + b ) ( b + a )
  1. Each diagram represents the square of an expression or a perfect square. Complete the cells in the last table by answering questions a–d.
Diagram 1 Diagram 2 Diagram 3
Diagram 1 Diagram 2 Diagram 3
  1. What is the answer for Cell a in Diagram 3?
  1. ( 1 3 ) 2
  2. ( 1 3 h ) 2
  3. h 2
  4. 1 3 h
  1. What is the answer for Cell b in Diagram 3?
  1. ( 1 3 ) 2
  2. ( 1 3 h ) 2
  3. h 2
  4. 1 3 h
  1. What is the answer for Cell c in Diagram 3?
  1. ( 1 3 ) 2
  2. ( 1 3 h ) 2
  3. h 2
  4. 1 3 h
  1. What is the answer for Cell d in Diagram 3?
  1. ( 1 3 ) 2
  2. ( 1 3 h ) 2
  3. h 2
  4. 1 3 h
  1. Rewrite the perfect-square expression ( h + 1 3 ) 2 in standard form a x 2 + b x + c .
  1. h 2 + 1 9 h + 2 3
  2. h 2 + 2 6 h + 2 6
  3. h 2 + 2 3 h + 1 9
  4. 2 h + 2 3 h + 1 9
  1. Rewrite the perfect-square expression ( 5 − m ) 2 in standard form a x 2 + b x + c .
  1. 25 m 2 − 10
  2. m 2 − 10 m + 25
  3. m 2 + 10 m − 25
  4. − 12 m + 10
  1. Rewrite the perfect-square expression ( n + 7 ) 2 in standard form a x 2 + b x + c .
  1. n 2 + 14 n + 49
  2. n 2 + 49 n + 14
  3. n 2 + 14 n + 14
  4. 16 n + 49

For 6 - 9, solve each equation, then choose the two solutions.

  1. ( x − 1 ) 2 = 4
  1. x = − 1
  2. x = 5
  3. x = 2
  4. x = 3
  5. x = 6
  1. ( x + 5 ) 2 = 81
  1. x = 76
  2. x = − 14
  3. x = 86
  4. x = 3
  5. x = 4
  1. ( x + 11 ) 2 = 121
  1. x = 132
  2. x = 110
  3. x = 0
  4. x = − 22
  5. x = 4
  1. ( x − 7 ) 2 = 64 49
  1. x = 2
  2. x = − 279 79
  3. x = 41 7
  4. x = 407 49
  5. x = 57 7
  1. Solve the equation ( x − 2 ) 2 = 0 .
PreviousNext
Order a print copy
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

© Aug 26, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.