# Let us simplify u

i. (a + b)(a – b)(a2 + ab + b2)(a2 – ab + b2)

= (a + b)(a2 – ab + b2)(a – b)(a2 + ab + b2)

Using x3 – y3 = (x – y)(x2 + xy + y2)

x3 + y3 = (x + y)(x2 – xy + y2)

= (a3 + b3)(a3 – b3)

Now, using (a + b)(a – b) = a2 – b2

= a6 – b6

ii. (a – 2b)(a2 + 2ab + 4b2)(a3 + 8b3)

= (a – 2b)(a2 + a(2b) + (2b)2)(a3 + (2b)3)

Using x3 – y3 = (x – y)(x2 + xy + y2)

x3 + y3 = (x + y)(x2 – xy + y2)

= (a3 – (2b)3)(a3 + (2b)3)

Now, using (a + b)(a – b) = a2 – b2

= a6 – (2b)6

= a6 – 64b6

iii. (4a2 – 9)(4a2 – 6a + 9)(4a2 + 6a + 9)

= [(2a)2 – 32](4a2 – 6a + 9)(4a2 + 6a + 9)

Using x2 – y2 = (x – y)(x + y)

= (2a – 3)(2a + 3)(4a2 – 6a + 9)(4a2 + 6a + 9)

= (2a – 3)(4a2 + 6a + 9)(2a + 3)(4a2 – 6a + 9)

Using x3 – y3 = (x – y)(x2 + xy + y2)

x3 + y3 = (x + y)(x2 – xy + y2)

= [(2a)3 – 33][(2a)3 + 33]

= (2a)6 - 36

= 64a6 – 729

iv. (x – y)(x2 + xy + y2) + (y – z)(y2 + yz + z2) + (z – x)(z2 + zx + x2)

Using a3 – b3 = (a – b)(a2 + ab + b2)

= x3 – y3 + y3 – z3 + z3 – x3

= 0

v. (x + 1)(x2 - x + 1) + (2x – 1)(4x2 + 2x + 1) – (x – 1)(x2 + x + 1)

= (x + 1)(x2 - x + 1) + (2x – 1)((2x)2 + 2x + 1) – (x – 1)(x2 + x + 1)

Using x3 – y3 = (x – y)(x2 + xy + y2)

x3 + y3 = (x + y)(x2 – xy + y2)

= x3 + 1 + (2x)3 – 1 - (x3 – 1)

= x3 + 1 + 8x3 – 1 – x3 + 1

= 8x3 + 1

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

<img src="https:/West Bengal - Mathematics

Let us write in tWest Bengal - Mathematics

Let us simplify uWest Bengal - Mathematics

Let’s find the vaWest Bengal - Mathematics

Let’s find the vaWest Bengal - Mathematics

Let’s resolve intWest Bengal - Mathematics

Let’s find the vaWest Bengal - Mathematics

Let us solve the West Bengal - Mathematics