Worksheet on Factoring Identities

Practice the worksheet on factoring identities to know how to factorize the algebraic identities using the formula of differences of squares and the formula of perfect square.

Follow the following three identities to factor the algebraic expressions:

(i) (a + b)² = a² + 2ab +b²,

(ii) (a - b)² = a² - 2ab + b² and

(iii) a² – b² = (a + b) (a – b).

Now using the above identities try to answer the following factors provided in the worksheet on factoring identities.  

1. Factor the given expressions using identity:

(i) m² + 8m + 16

(ii) 4x² – 4x + 1



(iii) x⁴ + 9y⁴ + 6x²y²

(iv) (a⁴ - 8a²b² + 16b⁴) - 18

(v) 256 – x² – 2xy – y²



2. Factorize the expressions:

(i) 4x² – 12xy + 9y²

(ii) 36x² – 84xy + 49y²

(iii) 9a² + 42ab + 49b²

(iv) (3a – 5b)² + 2 (3a – 5b ) (2b – a) + (2b - a)²

(v) 36x² + 36x + 8

(vi) 4a⁴ + b⁴



3. Factor the identities:

(i) 4x² + 12xy + 9y²

(ii) x² + 22x + 121

(iii) 9x² - 24xy + 16y²

(iv) 36x² - 36x + 9

(v) 16x⁴ - 72x²y² + 81y⁴

(vi) (a² + c² + 2ac) - b²



4. Factor completely using the formula:

(i) 100 – [121p² – 88pq + 16q²]

(ii) 36 - a² - b2 - 2ab

(iii) 25a² + 49b² -70ab – 15a + 21b

(iv) 4x² - 4x – 3

(v) 64 - a² – b² - 2ab

(vi) 25x² – (3y + 4z)²

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Answers for the worksheet on factoring identities are given below to check the exact answers of the above factorization.

Answers:

1. (i) (m + 4) (m + 4)  

(ii) (2x – 1) (2x – 1)  

(iii) (x² + 3y²) (x² + 3y²)

(iv) (a² - 4b² + 9) (a² - 4b² - 9)

(v) (16 + x + y) (16 - x - y)  

2. (i) (2x – 3y) (2x – 3y)  

(ii) (6x – 7y) (6x – 7y)  

(iii) (3a + 7b) (3a + 7b) 

(iv)  (2a - 3b) (2a - 3b)  

(v)  4(3x + 2) (3x + 1)

(vi) (2a² + b² + 2ab) (2a² + b² - 2ab)

3. (i) (2x + 3y) (2x + 3y)   

(ii) (x + 11) (x + 11) 

(iii) (3x - 4y) (3x - 4y)                         

(iv) 9(2x - 1) (2x - 1)

(v) (2x + 3y) (2x - 3y) (2x + 3y) (2x - 3y)   

(vi) (a + c + b) (a + c – b)   

 

4. (i) (10 + 11p - 4q) (10 - 11p + 4q)

(ii) (6 + a + b) (6 - a - b)   

(iii) (5a - 7b) (5a - 7b - 3)    

(iv) (2x + 1) (2x - 3)  

(v) (8 + a + b) (8 – a - b)   

(vi) (5x + 3y + 4z) (5x - 3y - 4z)

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