Compute Each Expression

[nycmath]

Precalculus
David Cohen
Edition 3
Chapter 3, Set 3.4

Compute each expression, given that the functions f, h, and m are defined as shown in the attachment.

[Eigenvalue]

8a. (h(f+m))(x)
=h(x)*(f+m)(x)
=x³(2x-1+x²-9)
=x⁵+2x⁴-10x³

[Eigenvalue]

8b. (hf)(x)+(hm)(x)
=x³(2x-1)+x³(x²-9)
=2x⁴-x³+x⁵-9x³
=x⁵+2x⁴-10x³

[nycmath]

8a. (h(f+m))(x)
=h(x)*(f+m)(x)
=x³(2x-1+x²-9)
=x⁵+2x⁴-10x³

Are you saying that 8a = 8b?

[nycmath]

8b. (hf)(x)+(hm)(x)
=x³(2x-1)+x³(x²-9)
=2x⁴-x³+x⁵-9x³
=x⁵+2x⁴-10x³

Are you saying that 8 a = 8b?

[Eigenvalue]

Yes, 8a=8b. I think that for (a(b+c))(x)=(ab)(x)+(ac)(x)