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 a2 - b2 = (a + b) (a – b).

1. Factorize the following by taking the difference of squares:

(i) x2 – 9

(ii) a2 – 1

(iii) 49 – x2

(iv) 4x2 – 25

(v) a2b2 – 16

(vi) a4 – b4



2. Factoring by the Difference of Two Perfect Squares:

(i) 144a2 – 169b2

(ii) 1 – 0.09a2

(iii) 16x2 – 121

(iv) – 64a2 + (9/25) b2

(v) x4 – 256

(vi) (x + y)4 – z4



3. Factorize using the formula of differences of two squares:

(i) 36a2 – b2

(ii) x2y2 – 16

(iii) 9a4b4 – 25p4q4

(iv) x4 – 256

(v) 81x2 – 49y2

(vi) x2 – (y – z)2



4. Factor the difference of two perfect squares:

(i) 16m2 – (3n + 2y)2

(ii) (3a + 4b)2 - (4b + 5b)2

(iii) (x + y)2 - (x – y)2

(iv) 50p2 – 72q2

(v) a4 - (b + c)4

(vi) m2 - 1/169



5. Factor each expression as a difference between two squares: (i) 9 (x + y)2 - 4 (x – y)2

(ii) 16/49 - 25p2

(iii) 9xy2 – x3

(iv) 4 (3x + 1)2 - 9 (x – 2)2

(v) 1 - 121a2

(vi) 169p2 - 1



6. Factor using the identity:

(i) 1 - (a + b)2

(ii) x2y2 - 25/z2

(iii) x12y4 - x4y12

(iv) 100 (x – y)2 – 121 (a + b)2

(v) 2x – 50x3

(vi) 25/x2 - (4x2)/9

(vii) x4 - 1/(y4)

(viii) 75x3y2 – 108xy4

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) (a2 + b2) (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) (x2 + 16) (x + 4) (x – 4)

(vi) [(x + y)2 + z2] (x + y + z) (x + y - z)


3. (i) (6a + b) (6a - b)                                                   

(ii) (xy + 4) (xy - 4)

(iii) (3a2b2 + 5p2q2) (3a2b2 - 5p2q2)

(iv) (x2 + 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) (a2 + b2 + c2 + 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) x4y4 (x4 + y4) (x2 + y2) (x + y) (x – y)

(iv) (10x - 10y + 11a + 11b) (10x - 10y - 11a - 11b)

(v) 2x (1 + 5x) (1 - 5x)

(vii) (x2 + 1/y2 ) (x + 1/y) (x - 1/y)

(viii) 3xy2 (5x + 6y) (5x - 6y)






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