Factorization
1. Factorization (1) (a + b ) (1 – c ) – (b + c ) ( 1 – c )
(2) 1 6 a2 + 40 a b + 25 b2
(3) 5x2yz - 5 x3y
(4) 18 q2 + 338 p2 - 1 5 6 p q
(5) -108 x2 - 363 y2 + 369 x y
2. Factorize
(1) 16- 4x2 (2) 20 x3 – 45 b4x
(2) 4a2 – 9 b2 – c2 - 6bc
(3) 25 ( x + 2y )2 - 36 (2x-5y)2
(4) 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 xy + 28 y z – 42 z x
(3) 4x6 + 9y6 + 16 x6 + 12 x6 y6 + 16 x3 z3 + 24 y3z3
(4) a8 + 256 b8 + 96 a4b4-16a3b2 – 256a2b6
4. Factorize using (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) 81a3 + 24b3
(3) 64a3b2 – 125 b5
(4) 16 a3 – 54 b3
(5) 8X3 + 1
(6) a3 - 27b3
(7) 729a6 - 1
(8) 8m3 + 64
(9) 1000 – 343 a9
(10) 8 + 64n3
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 x 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
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