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
2b
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
2y
2 – 16
(iii) 9a
4b
4 – 25p
4q
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
2y
2 - 25/z
2
(iii) x
12y
4 - x
4y
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
3y
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
2b
2 + 5p
2q
2) (3a
2b
2 - 5p
2q
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
4y
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
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