Question

Please help!! thank you.

Answer 1

(A) Product of
`-2x^(3)+x-5` and
`x^(3)-3x-4` is:

`(-2x^(3)+x-5)(x^(3)-3x-4)`

`=-2x^(3)(x^(3)-3x-4)+x(x^(3)-3x-4)-5(x^(3)-3x-4)`

`=(-2x^(3))(x^(3))+(-2x^(3))(-3x)+(-2x^(3))(-4)+x(x^(3))+(x)(-3x)+(x)(-4)+(-5)(x^(3))+(-5)(-3x)+(-5)(-4)`

`=-2x^(6)+6x^(4)+8x^(3)+x^(4)-3x^(2)-4x-5x^(3)+15x+20`

`=-2x^(6)+6x^(4)+x^(4)+ 8x^(3)-5x^(3)-3x^(2)-4x+15x+20`

`=-2x^(6)+7x^(4)+3x^(3)-3x^(2)+11x+20`

(B) Yes.

Product of
`-2x^(3)+x-5` and
`x^(3)-3x-4` = Product of
`x^(3)-3x-4` and
`-2x^(3)+x-5` because multiplication is commutative.

Commutative Property of multiplication says that a.b = b.a.

Thus, multiplication is same irrespective of the order of two numbers.