8th Factorization

1. Factorization

(1)   (a + b ) (1 – c ) – (b + c ) ( 1 – c )  (2)  1 6 a²   +  40 a b  + 25 b²         

(3)  4x²/9  - 2/3 x y +  y² /4

(4)    5x²yz   -    5 x³y                            (5)   18 q² + 338 p² -  1 5 6 p q         

(6)  -108 x² -  363 y² + 369 x y   

2.  Factorize  

(1)  16- 4x²                                          (2)   20 x³ – 45 b⁴x                             

(3)     4a² –  9 b²  –  c²  -  6bc

4)  25 ( x + 2y )²  - 36 (2x-5y)²           (5)   a² +  2 a b + b² – c2 -2cd –d²

3. Factorize using a²+b²+c² +2ab+2bc+2ca

(1)  x² + y² + 25 z² – 2 x y – 10 y z + 10 z x             (2)  9x²  +  4y² + 49z² –  12 x y  +  28 y z – 42  z x 

(3)   4x⁶ + 9y⁶ + 16 x ⁶ + 12 x³ y³ + 16 x³ z³ + 24 y³z³            (4)  a⁸ + 256 b⁸ + 96 a⁴b⁴-16a³b² – 256a²b⁶

4. Factorize (x + a) (x + b) = x² + (a + b) x +a b

(1) x²+7x+ 10              (2) x²+x-20                  (3) x²-4x-21     (4) 15x² + 13x + 2       (5) -6x² - 13x+5

5. Factorize

(1) 125 a³ + 150 a²b + 60 ab³ + 8ab³             (2)  x⁶ – 12 x⁴ b⁴ c + 6a²b⁵c² + b⁶c³  (3) 81a³ + 24b³          

(4) 64a³b² – 125 b⁵                             (5)  16 a³ – 54 b³                                 (6)  8X + 1      

(7) –a³  - 27b³                                      (8) 729a⁶ - 1    (9) 8m³ + 64                (10) 1000 – 343 a⁹

6. Find the following products:

(1)  (9m + 2m  )( 81m² -18mn + 4n²) (2) (5 - 2x ) (25 +10x + 4x²)      (3) (3 + 5/x ) ( 9 – 15/x + 25/x²)

7. Find the value of  27x² + 64y² + 36xy(3x + 4y) , when x = 5 and y = -3.

8. Using the identity (x + a) (x + b) = x²  + (a + b)x + a b, evaluate  98 ´ 97

9.  x + y + z = 0, prove that x ³+ y³ + z³ = 3xyz.

10. Factorize   

(1)  m⁴ – 256                           (2) y² –7y +12                         (3) 6xy – 4y + 6 – 9x

(4)  x⁴ – (y + z)⁴                             (5) a⁴ – 2a²b² + b⁴                            (6) (l + m) ² – 4lm

(7) (x² – 2xy + y²) – z²                        (8) 25a² – 4b² + 28bc – 49c²    (9) 5y² – 20y – 8z + 2yz

(10) a⁸ – b⁸