Worksheet on Factoring the Differences of Two Squares
Worksheet on factoring the differences of two squares will help us to factorize an algebraic expression using the following identity a
^{2}  b
^{2} = (a + b) (a – b).
1. Factorize the following by taking the difference of squares:
(i) x
^{2} – 9
(ii) a
^{2} – 1
(iii) 49 – x
^{2}
(iv) 4x
^{2} – 25
(v) a
^{2}b
^{2} – 16
(vi) a
^{4} – b
^{4}
2. Factoring by the Difference of Two Perfect Squares:
(i) 144a
^{2} – 169b
^{2}
(ii) 1 – 0.09a
^{2}
(iii) 16x
^{2} – 121
(iv) – 64a
^{2} + (9/25) b
^{2}
(v) x
^{4} – 256
(vi) (x + y)
^{4} – z
^{4}
3. Factorize using the formula of differences of two squares:
(i) 36a
^{2} – b2
(ii) x
^{2}y
^{2} – 16
(iii) 9a
^{4}b
^{4} – 25p
^{4}q
^{4}
(iv) x
^{4} – 256
(v) 81x
^{2} – 49y
^{2}
(vi) x
^{2} – (y – z)
^{2}
4. Factor the difference of two perfect squares:
(i) 16m
^{2} – (3n + 2y)
^{2}
(ii) (3a + 4b)
^{2}  (4b + 5b)
^{2}
(iii) (x + y)
^{2}  (x – y)
^{2}
(iv) 50p
^{2} – 72q
^{2}
(v) a
^{4}  (b + c)
^{4}
(vi) m
^{2}  1/169
5. Factor each expression as a difference between two squares:
(i) 9 (x + y)
^{2}  4 (x – y)
^{2}
(ii) 16/49  25p
^{2}
(iii) 9xy
^{2} – x
^{3}
(iv) 4 (3x + 1)
^{2}  9 (x – 2)
^{2}
(v) 1  121a
^{2}
(vi) 169p
^{2}  1
6. Factor using the identity:
(i) 1  (a + b)
^{2}
(ii) x
^{2}y
^{2}  25/z
^{2}
(iii) x
^{12}y
^{4}  x
^{4}y
^{12}
(iv) 100 (x – y)
^{2} – 121 (a + b)
^{2}
(v) 2x – 50x
^{3}
(vi) 25/x
^{2}  (4x
^{2})/9
(vii) x
^{4}  1/(y
^{4})
(viii) 75x
^{3}y
^{2} – 108xy
^{4}
Answers for the worksheet
on factoring the differences of two squares are given below to check the exact
answers of the above factorization.
Answers:
1. (i) (x + 3) (x
 3)
(ii) (a + 1) (a  1)
(iii) (7 + x) (7  x)
(iv) (2x + 5) (2x  5)
(v) (ab + 4) (ab  4)
(vi) (a
^{2} + b
^{2}) (a + b) (a  b)
2. (i) (12a +
13b) (12a  13b)
(ii) (1 + 0.3a) (1  0.3a)
(iii) (4x + 11) (4x  11)
(iv) [(3/5)b + 8a] [(3/5)b  8a]
(v) (x
^{2} + 16) (x + 4) (x – 4)
(vi) [(x + y)
^{2} + z
^{2}] (x + y + z) (x + y  z)
3. (i) (6a + b)
(6a  b)
(ii) (xy + 4) (xy  4)
(iii) (3a
^{2}b
^{2} + 5p
^{2}q
^{2}) (3a
^{2}b
^{2}  5p
^{2}q
^{2})
(iv) (x
^{2} + 16) (x + 4) (x  4)
(v) (9x + 7y) (9x  7y)
(vi) (x + y  z) (x – y + z)
4. (i) (4m + 3n +
2y) (4m  3n  2y)
(ii) (3a + 8b + 5d)
(3a – 5d)
(iii) 4xy
(iv) 2(5p + 6q) (5p  6q)
(v) (a
^{2} + b
^{2} + c
^{2} + 2bc) (a + b + c) (a – b  c)
(vi) (m + 1/13) (m  1/13)
5. (i) (5x + y)
(x + 5y)
(ii) (4/7 + 5p) (4/7  5p)
(iii) x(3y + x) (3y  x)
(iv) (9x – 4) (3x + 8)
(v) (1 + 11a) (1  11a)
(vi) (13p + 1) (13p  1)
6. (i) (1 + a +
b) (1 – a  b)
(ii) (xy + 5/z) (xy  5/z)
(iii) x
^{4}y
^{4} (x
^{4} + y
^{4}) (x
^{2} + y
^{2}) (x + y) (x – y)
(iv) (10x  10y + 11a + 11b) (10x  10y  11a  11b)
(v) 2x (1 + 5x) (1  5x)
(vii) (x
^{2} + 1/y
^{2} ) (x + 1/y) (x  1/y)
(viii) 3xy
^{2} (5x + 6y) (5x  6y)
8th Grade Math Practice
Math Homework Sheets
From Worksheet on Factoring the Differences of Two Squares to HOME PAGE
Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.
Share this page:
What’s this?


New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.