Find the coefficient of w^2x^2y^2z^2, in the expansion of (a) (2w- x+3y+z-2)^12 (b)(v+w-2x+y+5z+3)^12

Answer 1

The Expression is (2w - x +3y + z - 2)^12.

We can solve this expression using Multinomial Theorem.

Multinomial Theorem is given by

Where n is the order of the expression

where .

  is the Multinomial coefficient.

Now to find the coefficient of w²x²y²z²,

The term w²x²y²z² is

= 718,502,400 w²x²y²z².

Therefore the coefficient of w²x²y²z² is 718502400.

Answer 2

(b)

The Expression is (v+w - 2x +y + 5z + 3)^12.

We can solve this expression using Multinomial Theorem.

Multinomial Theorem is given by

Where n is the order of the expression

where .

  is the Multinomial coefficient.

Now to find the coefficient of w²x²y²z²,

The term w²x²y²z² is

= 10,103,940,000 w²x²y²z².

Therefore the coefficient of w²x²y²z² is 10103940000.