Advertisements
Advertisements
प्रश्न
The value of (a + 1)(a – 1)(a2 + 1) is a4 – 1.
पर्याय
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
Solving it, we get
(a + 1)(a – 1)(a2 + 1) = {(a + 1)(a – 1)} × (a2 + 1)
⇒ (a + 1)(a – 1)(a2 + 1) = (a2 – 1)(a2 + 1) ...[∵ (x + y)(x – y) = x2 – y2; Put x = a and y = 1 ⇒ (a + 1)(a – 1) = a2 – 1]
⇒ (a + 1)(a – 1)(a2 + 1) = a4 – 1 ...[∵ (x2 + y2)(x2 – y2) = x4 – y4; Put x = a and y = 1 ⇒ (a2 + 1)(a2 – 1) = a4 – 1]
Thus, the value of (a + 1)(a – 1)(a2 + 1) is a4 – 1.
APPEARS IN
संबंधित प्रश्न
Factorise the following expressions
m2 + m – 72
Using the identity (a + b)(a – b) = a2 – b2, find the following product
(1 + 3b)(3b – 1)
Multiply the following:
(a2 – b2), (a2 + b2)
Using suitable identities, evaluate the following.
(339)2 – (161)2
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
28ay2 – 175ax2
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
`x^2/8 - y^2/18`
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
(a – b)2 – (b – c)2
The sum of (x + 5) observations is x4 – 625. Find the mean of the observations.
The base of a parallelogram is (2x + 3 units) and the corresponding height is (2x – 3 units). Find the area of the parallelogram in terms of x. What will be the area of parallelogram of x = 30 units?
Verify the following:
(a + b + c)(a2 + b2 + c2 – ab – bc – ca) = a3 + b3 + c3 – 3abc
