Advertisements
Advertisements
प्रश्न
Factorize the following expressions:
(a + b)3 – 8(a – b)3
Advertisements
उत्तर
(a + b)3 - 8(a - b)3
= (a + b)3 - [2(a - b)]3
= (a + b)3 - (2a - 2b)3 [Using a3 - b3 = (a - b)(a2 + ab + b2 ) ]
= (a + b - (2a - 2b))((a + b)2 + (a + b)(2a - 2b) + (2a - 2b)2)
= (a + b - 2a + 2b)(a2 + b2 + 2ab + (a + b)(2a - 2b) + (2a - 2b)2) [∵ (a + b)2 = a2 + b2 + 2ab]
= (3b - a)(a2 + b2 + 2ab + 2a2 - 2ab + 2ab - 2b2 + (2a - 2b)2)
= (3b - a)(3a2 + 2ab - b2 + (2a - 2b)2 )
= (3b - a)(3a2 + 2ab - b2 + 4a2 + 4b2 - 8ab) [∵ (a - b)2 = a2 + b2 - 2ab]
= (3b - a )(3a2 + 4a2 - b2 + 4b2 + 2ab - 8ab)
= (3b - a )(7a2 + 3b2 - 6ab)
∴ (a + b)3 - 8(a - b)3 = (-a + 3b)(7a2 - 6ab + 3b2)
APPEARS IN
संबंधित प्रश्न
Factorize (a - b + c)2 + (b - c + a)2 + 2(a - b + c) (b - c + a)
Given possible expressions for the length and breadth of the rectangle having 35y2 + 13y – 12 as its area.
Factorize the following expressions:
`x^3/216 - 8y^3`
Factorize the following expressions:
a3 + b3 + a + b
Simplify `(155 xx 155 xx 155 - 55 xx 55 xx 55)/(155 xx 155 + 155 xx 55 + 55 xx 55)`
Factorize 64a3 +125b3 + 240a2b + 300ab2
Factorize : x2 − 1 − 2a − a2
(x + y)3 − (x − y)3 can be factorized as
Divide: 6x2 + 5x - 6 by 2x + 3
Which of the following is an example of a monomial?
