Difference of Squares and Perfect-Square Trinomials

Question 1

Factor 49x^2 - 64 completely.

Accepted Answer

(7x + 8)(7x - 8)

Answer

(7x - 8)^2

Answer

(7x + 8)^2

Answer

(7x + 64)(7x - 64)

Question 2

Which statement about k^2 + 121 is correct?

Accepted Answer

it does not factor over the real numbers, because it is a SUM of two squares

Answer

it factors as (k + 11)(k - 11), in the same way as a difference of squares

Answer

it factors as (k + 11)^2, because both of its terms are perfect squares

Answer

it factors as (k - 11)^2, because both of its terms are perfect squares

Question 3

Which pattern does m^2 + 18m + 77 fit?

Accepted Answer

none of these patterns

Answer

a difference of two squares

Answer

a perfect-square trinomial

Answer

a sum of two squares

Question 4

Factor 16b^2 - 88b + 121 completely.

Accepted Answer

(4b - 11)^2

Answer

(4b + 11)^2

Answer

(4b + 11)(4b - 11)

Answer

(4b - 88)^2

Question 5

Factor 49p^2 - 36 completely.

Accepted Answer

(7p + 6)(7p - 6)

Answer

(7p - 6)^2

Answer

(7p + 6)^2

Answer

(7p + 36)(7p - 36)

Question 6

Factor b^2 - 121 completely.

Accepted Answer

(b + 11)(b - 11)

Answer

(b - 11)^2

Answer

(b + 11)^2

Answer

(b + 121)(b - 121)

Question 7

Factor w^2 - 16w + 64 completely.

Accepted Answer

(w - 8)^2

Answer

(w + 8)^2

Answer

(w + 8)(w - 8)

Answer

(w - 16)^2

Question 8

Which pattern does b^2 - 100 fit?

Accepted Answer

a difference of two squares

Answer

a perfect-square trinomial

Answer

a sum of two squares

Answer

none of these patterns

Question 9

Factor 4k^2 - 28k + 49 completely.

Accepted Answer

(2k - 7)^2

Answer

(2k + 7)^2

Answer

(2k + 7)(2k - 7)

Answer

(2k - 28)^2

Question 10

Which pattern does m^2 + 22m + 121 fit?

Accepted Answer

a perfect-square trinomial

Answer

a difference of two squares

Answer

a sum of two squares

Answer

none of these patterns

Question 11

Factor 25n^2 - 16 completely.

Accepted Answer

(5n + 4)(5n - 4)

Answer

(5n - 4)^2

Answer

(5n + 4)^2

Answer

(5n + 16)(5n - 16)

Question 12

Which pattern does p^2 + 121 fit?

Accepted Answer

a sum of two squares

Answer

a difference of two squares

Answer

a perfect-square trinomial

Answer

none of these patterns

Question 13

Factor 9y^2 - 24y + 16 completely.

Accepted Answer

(3y - 4)^2

Answer

(3y + 4)^2

Answer

(3y + 4)(3y - 4)

Answer

(3y - 24)^2

Question 14

Factor x^2 - 64 completely.

Accepted Answer

(x + 8)(x - 8)

Answer

(x - 8)^2

Answer

(x + 8)^2

Answer

(x + 64)(x - 64)

Question 15

Factor 49m^2 - 25 completely.

Accepted Answer

(7m + 5)(7m - 5)

Answer

(7m - 5)^2

Answer

(7m + 5)^2

Answer

(7m + 25)(7m - 25)

Question 16

Which statement about h^2 + 9 is correct?

Accepted Answer

it does not factor over the real numbers, because it is a SUM of two squares

Answer

it factors as (h + 3)(h - 3), in the same way as a difference of squares

Answer

it factors as (h + 3)^2, because both of its terms are perfect squares

Answer

it factors as (h - 3)^2, because both of its terms are perfect squares

Question 17

Factor 49p^2 - 154p + 121 completely.

Accepted Answer

(7p - 11)^2

Answer

(7p + 11)^2

Answer

(7p + 11)(7p - 11)

Answer

(7p - 154)^2

Question 18

Factor 9w^2 - 100 completely.

Accepted Answer

(3w + 10)(3w - 10)

Answer

(3w - 10)^2

Answer

(3w + 10)^2

Answer

(3w + 100)(3w - 100)

Question 19

Factor 25r^2 - 49 completely.

Accepted Answer

(5r + 7)(5r - 7)

Answer

(5r - 7)^2

Answer

(5r + 7)^2

Answer

(5r + 49)(5r - 49)

Question 20

Factor 16t^2 + 40t + 25 completely.

Accepted Answer

(4t + 5)^2

Answer

(4t + 5)(4t - 5)

Answer

(4t + 40)^2

Answer

(4t + 1)(4t + 25)

Question 21

Factor 49k^2 + 70k + 25 completely.

Accepted Answer

(7k + 5)^2

Answer

(7k + 5)(7k - 5)

Answer

(7k + 70)^2

Answer

(7k + 1)(7k + 25)

Question 22

Which statement about 25w^2 + 9 is correct?

Accepted Answer

it does not factor over the real numbers, because it is a SUM of two squares

Answer

it factors as (5w + 3)(5w - 3), in the same way as a difference of squares

Answer

it factors as (5w + 3)^2, because both of its terms are perfect squares

Answer

it factors as (5w - 3)^2, because both of its terms are perfect squares

Question 23

Factor 16n^2 - 121 completely.

Accepted Answer

(4n + 11)(4n - 11)

Answer

(4n - 11)^2

Answer

(4n + 11)^2

Answer

(4n + 121)(4n - 121)

Question 24

Factor 16a^2 + 88a + 121 completely.

Accepted Answer

(4a + 11)^2

Answer

(4a + 11)(4a - 11)

Answer

(4a + 88)^2

Answer

(4a + 1)(4a + 121)

Question 25

Which pattern does n^2 + 8n + 16 fit?

Accepted Answer

a perfect-square trinomial

Answer

a difference of two squares

Answer

a sum of two squares

Answer

none of these patterns

Question 26

Factor r^2 - 25 completely.

Accepted Answer

(r + 5)(r - 5)

Answer

(r - 5)^2

Answer

(r + 5)^2

Answer

(r + 25)(r - 25)

Question 27

Which pattern does b^2 + 20b + 121 fit?

Accepted Answer

none of these patterns

Answer

a perfect-square trinomial

Answer

a difference of two squares

Answer

a sum of two squares

Question 28

Factor m^2 - 22m + 121 completely.

Accepted Answer

(m - 11)^2

Answer

(m + 11)^2

Answer

(m + 11)(m - 11)

Answer

(m - 22)^2

Question 29

Which statement about 25r^2 + 49 is correct?

Accepted Answer

it does not factor over the real numbers, because it is a SUM of two squares

Answer

it factors as (5r + 7)(5r - 7), in the same way as a difference of squares

Answer

it factors as (5r + 7)^2, because both of its terms are perfect squares

Answer

it factors as (5r - 7)^2, because both of its terms are perfect squares

Question 30

Factor 64r^2 - 9 completely.

Accepted Answer

(8r + 3)(8r - 3)

Answer

(8r - 3)^2

Answer

(8r + 3)^2

Answer

(8r + 9)(8r - 9)

Question 31

Factor t^2 - 10t + 25 completely.

Accepted Answer

(t - 5)^2

Answer

(t + 5)^2

Answer

(t + 5)(t - 5)

Answer

(t - 10)^2

Question 32

Which pattern does w^2 - 16 fit?

Accepted Answer

a difference of two squares

Answer

a perfect-square trinomial

Answer

a sum of two squares

Answer

none of these patterns

Question 33

Which statement about 9x^2 + 25 is correct?

Accepted Answer

it does not factor over the real numbers, because it is a SUM of two squares

Answer

it factors as (3x + 5)(3x - 5), in the same way as a difference of squares

Answer

it factors as (3x + 5)^2, because both of its terms are perfect squares

Answer

it factors as (3x - 5)^2, because both of its terms are perfect squares

Question 34

Factor y^2 - 14y + 49 completely.

Accepted Answer

(y - 7)^2

Answer

(y + 7)^2

Answer

(y + 7)(y - 7)

Answer

(y - 14)^2

Question 35

Factor 25x^2 - 49y^2 completely.

Accepted Answer

(5x + 7y)(5x - 7y)

Answer

(5x - 7y)^2

Answer

(5x + 7y)^2

Answer

(25x + 49y)(25x - 49y)

Question 36

Which statement about w^2 + 49 is correct?

Accepted Answer

it does not factor over the real numbers, because it is a SUM of two squares

Answer

it factors as (w + 7)(w - 7), in the same way as a difference of squares

Answer

it factors as (w + 7)^2, because both of its terms are perfect squares

Answer

it factors as (w - 7)^2, because both of its terms are perfect squares

Question 37

Factor 16a^2 - 25 completely.

Accepted Answer

(4a + 5)(4a - 5)

Answer

(4a - 5)^2

Answer

(4a + 5)^2

Answer

(4a + 25)(4a - 25)

Question 38

Factor 49b^2 - 112b + 64 completely.

Accepted Answer

(7b - 8)^2

Answer

(7b + 8)^2

Answer

(7b + 8)(7b - 8)

Answer

(7b - 112)^2

Question 39

Which pattern does n^2 + 16 fit?

Accepted Answer

a sum of two squares

Answer

a difference of two squares

Answer

a perfect-square trinomial

Answer

none of these patterns

Question 40

Factor 36a^2 - 25b^2 completely.

Accepted Answer

(6a + 5b)(6a - 5b)

Answer

(6a - 5b)^2

Answer

(6a + 5b)^2

Answer

(36a + 25b)(36a - 25b)

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Difference of Squares and Perfect-Square Trinomials

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Difference of Squares and Perfect-Square Trinomials

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner