Advertisements
Advertisements
Question
Factorize the following expressions:
(a - 2b)3 - 512b3
Advertisements
Solution
(a - 2b)3 - 512b3
= (a - 2b)3 - (8b)3
= (a - 2b - 8b)((a - 2b)2 + (a - 2b)8b + (8b)2) [ ∵ a3 - b3 = (a - b)(a2 + ab + b2)]
= (a -10b)(a2 + 4b2 - 4ab + 8b (a - 2b) + (8b)2 ) [ ∵ (a - b)2 = a2 + b2 - 2ab]
= (a -10b)(a2 + 4b2 - 4ab + 8ab -16b2 + 64b2)
= (a = 10b)(a2 + 68b2 -16b2 - 4ab + 8ab)
= (a -10b)(a2 + 52b2 + 4ab)
∴ (a - 2b)3 - 512b3 = (a -10b)(a2 + 4ab + 52b2)
APPEARS IN
RELATED QUESTIONS
Factorize x( x - 2)( x - 4) + 4x - 8
Factorize 4( x - y)2 -12( x - y)( x + y ) + 9(x + y )2
Factorize the following expressions:
p3 + 27
`2sqrt2a^3 + 3sqrt3b^3 + c^3 - 3 sqrt6abc`
8x3 -125y3 +180xy + 216
(x + y)3 − (x − y)3 can be factorized as
Evaluate: (a2 + 2ab + b2)(a + b)
Divide: - 16ab2c by 6abc
If x = 2 and y = 3, then find the value of the following expressions
x + 1 – y
Express the following properties with variables x, y and z.
Commutative property of multiplication
