Advertisements
Advertisements
प्रश्न
Factorize a3 – 3a2b + 3ab2 – b3 + 8
Advertisements
उत्तर
a3 - 3a2b + 3ab2 - b3 + 8
= (a - b)3 + 8 [∵ a3 - b3 - 3a2b + 3ab2 = (a - b)3
= (a - b)3 + 23
= (a - b + 2)((a - b)2 - (a - b)2 + 22 ) [∵ a3 + b3 = (a + b)(a2 - ab + b2)]
= (a - b + 2)(a2 + b2 - 2ab - 2(a - b) + 4)
= (a - b + 2)(a2 + b2 - 2ab - 2a + 2b + 4)
∴ a3 - 3a2b + 3ab2 - b3 + 8 = (a - b + 2)(a2 + b2 - 2ab - 2a + 2b + 4)
APPEARS IN
संबंधित प्रश्न
Factorize: a2 + b2 + 2 (ab + bc + ca)
Factorize `x^2 + 2sqrt3x - 24`
Factorize `9(2a - b)^2 - 4(2a - b) - 13`
Factorize x3 -12x ( x - 4) - 64
8x3 + 27y3 - 216z3 + 108xyz
Find the value of x3 + y3 − 12xy + 64, when x + y =−4
Multiply: (xy + 2b)(xy - 2b)
Divide: 6x2 + 5x - 6 by 2x + 3
Divide: 15x2 + 31xy + 14y2 by 5x + 7y
Divide: x3 − 6x2 + 11x − 6 by x2 − 4x + 3
