Free Printable Alg 2: Difference Between Two Squares

1.

1) Factor: $25x^2-16$

a)

(5x - 2)(5x + 2)

b)

(25x - 16)(1)

c)

(5x - 8)(5x + 8)

d)

(10x - 4)(2.5x + 4)

e)

(5x - 4)(5x + 4)

2.

2) Factor: $9x^2-121$

a)

(9x + 121)(x - 1)

b)

(3x - 1)(3x + 1)

c)

(3x - 12)(3x + 12)

d)

(3x - 11)(3x + 11)

e)

(9x - 11)(x + 11)

3.

3) Factor $36x^2-25$

a)

(9x - 5)(4x + 5)

b)

(6x - 5)(6x + 5)

c)

(2x - 1)(18x + 25)

d)

(6x - 6)(6x + 6)

e)

(12x - 3)(3x + 3)

4.

Is this a perfect square trinomial?
x² + 16x + 64

a)

Yes

b)

No

5.

4) Factor $81x^2-169$

a)

(3x - 13)(27x + 13)

b)

(9x - 1)(9x + 1)

c)

(81x - 169)

d)

(9x - 13)(9x + 13)

e)

(27x - 13)(3x + 13)

6.

5) Factor $9a^4-81b^2$

a)

(3a^2 - 3b)(3a^2 + 3b)

b)

3(3a^2 - 27b)(3a^2 + 27b)

c)

(3a^2 - 9b)(3a^2 + 9b)

d)

9(a^4 - 9b^2)

e)

9(a^2 - 3b)(a^2 + 3b)

7.

6) Factor $64c^4-81r^2$

a)

(4c^2 - 9r)(16c^2 + 9r)

b)

(8c^2 - 3r)(8c^2 + 3r)

c)

(16c^2 - 9r)(4c^2 + 9r)

d)

(8c^2 - 9r)(8c^2 + 9r)

e)

(2c^2 - 9r)(32c^2 + 9r)

8.

Is this a perfect square trinomial?
x² + 14x + 49

a)

Yes

b)

No

9.

7) Factor $49u^4-225z^2$

a)

(7u^2 - 15z)(7u^2 - 15z)

b)

(49u^4 + 225z^2)

c)

(49u^2 - 225z)(u^2 + z)

d)

(7u^2 - 15z)(7u^2 + 15z)

e)

(7u^2 + 15z)(7u^2 + 15z)

10.

8) Factor $400b^4-9c^2$

a)

(40b^2 - 3c)(10b^2 + 3c)

b)

(10b^2 - 3c)(40b^2 + 3c)

c)

(20b^2 - 9c)(20b^2 + 9c)

d)

(25b^2 - 3c)(16b^2 + 3c)

e)

(20b^2 - 3c)(20b^2 + 3c)

11.

9) Factor $\left(d-1\right)^2-49$

a)

(d - 1)(d - 49)

b)

(d - 5)(d + 5)

c)

(d - 8)(d + 6)

d)

(d - 7)(d + 7)

e)

(d - 6)(d - 8)

12.

10) Factor $\left(y+2\right)^2-36$

a)

(y - 4)(y + 8)

b)

(y - 2)(y + 10)

c)

(y + 2)(y - 18)

d)

(y - 6)(y + 6)

e)

(y + 4)(y + 8)

13.

Is this a perfect square trinomial?
x² + 6x + 25

a)

Yes

b)

No

14.

11) Factor $\left(3g-2\right)^2-16k^2$

a)

(3g - 4 - 4k)(3g + 4 + 4k)

b)

(3g + 2 - 4k)(3g + 2 + 4k)

c)

(3g - 2 - 4k)(3g - 2 + 4k)

d)

(3g - 2 - 2k)(3g - 2 + 2k)

e)

(3g - 2 - 8k)(3g - 2 + 8k)

15.

12) Factor $9n^2-6np+p^2$

a)

(3n - 3p)(3n + p)

b)

(9n^2 + 6np + p^2)

c)

(3n - p)(3n - p)

d)

(9n - p)(n + p)

e)

(3n + p)^2

16.

Is this a perfect square trinomial?
x² + 18x + 9

a)

Yes

b)

No

17.

13) Factor $x^4+4x^2y+4y^2$

a)

(x^2 - 2y)^2

b)

(x^2 + 4y)^2

c)

(x^2 - 4y)^2

d)

(x^2 + 2y)^2

e)

(x^2 + 2y + 1)(x^2 + 2y - 1)

18.

14) Factor $4a^4-4a^2c+c^2$

a)

(4a^4 + 4a^2c + c^2)

b)

(4a^2 - c)^2

c)

(2a^2 + c)^2

d)

(2a^2 - 2c)(2a^2 + 2c)

e)

(2a^2 - c)^2

19.

Is this a perfect square trinomial?
x² + 10x + 100

a)

Yes

b)

No

20.

x² - 9

a)

(x + 3)²

b)

(x + 3) (x - 3)

c)

(x - 3)²

d)

x + 3(x - 3)

21.

x² - 16

a)

(x + 4) (x - 4)

b)

(x + 8) (x - 2)

c)

(x + 4)²

d)

x + 4(x - 4)

22.

4x² - 25

a)

(2x + 5) (2x - 5)

b)

(2x - 5)²

c)

(2x + 5)²

d)

2x + 5(2x - 5)

23.

25x² - 36y²

a)

5x + 6y(5x - 6y)

b)

(5x + 6y) (5x - 6y)

c)

(5x + 6y)²

d)

(5x - 6y)²

24.

4x²y² - 1

a)

(2 + xy) (2 - xy)

b)

(2x + y) (2x - y)

c)

(2xy + 1) (2xy - 1)

d)

(2y + x) (2y - x)

25.

64x² - 81y²

a)

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

b)

(8x + 9y) (8x - 9y)

c)

(6x + 7y) (6x - 7y)

d)

(6x + 9y) (6x - 9y)

26.

4x² - 16

a)

4(2x + 4) (x - 2)

b)

4(4x + 2) (x - 2)

c)

(2x + 4) (2x - 4)

d)

4(x + 2) (x - 2)

27.

49x² - 144y²

a)

(7x + 16y) (7x - 16y)

b)

(7x + 12y)²

c)

(12x + 7y) (12x - 7y)

d)

(7x + 12y) (7x - 12y)

28.

Factor 4y² – 9.

a)

(2y + 3)(2y – 3)

b)

prime

c)

(2y + 3)(2y + 3)

d)

(2y – 3)(2y – 3)

29.

Factor completely.

x² - 144

a)

( x - 12 ) ²

b)

( x - 12 ) ( x - 12 )

c)

( x + 12 ) ( x + 12 )

d)

( x + 12 ) ( x - 12 )

30.

Factor completely.

y² - 196

a)

( y - 14 ) ( y - 14 )

b)

( y + 14 ) ( y - 14 )

c)

( y + 13 ) ( y - 13 )

d)

( y - 13 ) ²

31.

Factor completely.

121x² - 49

a)

( 11x - 7 ) ²

b)

( 11x - 7 ) ( 11x - 7 )

c)

( 11x + 7 ) ( 11x - 7 )

d)

( 12x + 7 ) ( 12x - 7 )

32.

Factor completely.

64x² - 49y²

a)

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

b)

( 8x - 7y ) ( 8x - 7y )

c)

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

d)

( 8x - 7y )²

33.

Factor completely.

225x² - 169y²

a)

( 15x - 13y )²

b)

( 15x + 13 ) ( 15x - 13 )

c)

( 25x + 13y ) ( 25x - 13y )

d)

( 15x + 13y ) ( 15x - 13y )

34.

Factor completely.

49x² + 16

a)

( 7x + 4 ) ( 7x - 4 )

b)

( 7x + 4 ) ( 7x + 4 )

c)

( 7x - 4 ) ²

d)

does not factor (SUM of squares)

35.

Which of these can factor using difference of two squares?

a)

144x² - 49y²

b)

x² + 4x - 12

c)

100x² + 20x + 1

d)

14x - 16

36.

We can't factor using difference of two square this

49x² + 4y². Why?

a)

Because 4 is not a perfect cubed number.

b)

Because 4 is not a perfect squared number.

c)

Because 49 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

37.

Factor x²-25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

38.

Fully Factor the Following
25x²-81

a)

(5x-9)²

b)

(5x+9)(5x-9)

c)

25(x-9)²

d)

(9x+5)(9x-5)

39.

49n² - 25

a)

Not Factorable

b)

(3n + 5)(3n - 5)

c)

(7n + 5)(7n - 5)

d)

(5n + 7)(5n - 7)

40.

(x+2)(x−2)

a)

x²−4x−4

b)

x²+4

c)

x²−4

d)

x²+4x−4

41.

(x+7)(x−7)

a)

x²−14x−49

b)

x²−49

c)

x²+49

d)

x²+14x−49

42.

Find the product:

(x + 12)(x - 12)

a)

x² - 144

b)

x² + 144

c)

x² + 12x - 144

d)

x² - 12x + 144

43.

When you multiply (x - 10)(x + 10), how many terms will the answer have?

a)

one term

b)

two terms

c)

three terms

44.

Find the product:
(x + 12)(x - 12)

a)

x² - 144

b)

x² + 144

c)

x² + 12x - 144

d)

x² - 12x + 144

45.

Multiply:
(r + 7)(r − 7)

a)

r ²− 49

b)

r ²+ 14

c)

r ² − 7r + 49

46.

Find the product:
(3x + 2)(2x + 4)

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

47.

REVIEW: Multiply the monomials:

2x³ ⋅ 5x³

a)

7x³

b)

10x⁶

c)

10x⁹

d)

15x³

e)

10x³

48.

REVIEW: Simplify

(7x⁴y³z^-3qr)⁰

a)

pi

b)

1

c)

0

d)

7x⁴y³z^-3qr

49.

Which is quadratic?

a)

x³ + x² + 5

b)

x^quadratic

c)

x² - 1

d)

q⁴ + 2q + q + 4

50.

$(x+y)(x−y)=x^2−y^2$

a)

TRUE

b)

FALSE

Alg 2: Difference Between Two Squares

Total questions: 50

Worksheet time: 6hrs 7mins

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