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

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