Q. 115.0( 1 Vote )

Simplify:

(i) (2x + y + 4z)(4x2 + y2 + 16z2 – 2xy – 4yz – 8zx)

(ii) (x – 3y – 5z)(x2 + 9y2 + 25z2 + 3xy – 15yz + 5zx)

Answer :

(i) (2x + y + 4z) (4x2 + y2 + 16z2 – 2xy – 4yz – 8zx)


Here the identity used is


a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – bc – ac)


Comparing this with given condition


(2x + y + 4z) (4x2 + y2 + 16z2 – 2xy – 4yz – 8zx) = (2x)3 + y3 + (4z)3 – 3 × 2x × y × 4z


8x3 + y3 + 64z3 – 24xyz


(ii) (x – 3y – 5z)(x2 + 9y2 + 25z2 + 3xy – 15yx + 5zx)


Here the identity used is


a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – bc – ac)


Comparing this with given condition


(x – 3y – 5z)(x2 + 9y2 + 25z2 + 3xy – 15yx + 5zx)


= x3 + (– 3y)3 + (– 5z)3 – 3(x) (– 3y)(– 5z)


= x3 – 27y3 – 125z3 – 45xyz


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
caricature
view all courses