help me! with a math problem! please?

Solve this like you'd do this type with FOIL:

(x + y) (a + b)

except here, you have:

(x + y + z)(a + b + c)

Same thing. You take your x and multiply it through a, b, and c, then you do the same with y and the same with z:

(3x +7w +4) (4x - 5w - 2)
12x² - 15wx - 6x + 28wx - 35w² - 14w + 16x - 20w - 8
12x² + 13wx + 10x - 35w² - 34w - 8

(3x + 7w + 4)(4x - 5w - 2)
= 3x*4x + 7w*4x + 4*4x - 3x*5w - 7w*5w - 4*5w - 2*3x - 7w*2 - 4*2
= 12x^2 + 28wx + 16x - 15wx - 35w^2 - 20w - 6x - 14w - 8
= 12x^2 + 16x - 6x + 28wx - 15wx - 35w^2 - 20w - 14w - 8
= 12x^2 + 10x + 13wx - 35w^2 - 34w - 8

(3x +7w +4) (4x - 5w - 2).
= 3x (4x - 5w - 2) + 7 w (4x - 5w - 2) + 4(4x - 5w - 2).
= 12x² - 15xw - 6x + 28xw - 35w² - 14w + 16x -20w - 8
= 12x² + 13xw + 10x - 35w² - 34w - 8

(3x +7w +4) (4x - 5w - 2) =

12x^2 - 15xw - 6x + 28xw - 35w^2 - 14w +16x - 20w - 8 =

12x^2 - 35w^2 + 13xw + 10x - 34w - 8

(3x +7w +4) (4x - 5w - 2).
=12x^2 - 15wx -6x +28wx - 35w^2 -14w + 16x -20w -8
= 12x^2 -35w^2 + 13wx + 10x -34w -8
(",)

checking
(3+7+4)(4-5-2)=-42
12-35+13+10-34-8=-42

12x - 35w -8

7x+2w+2 i think i mean thats how we learned it in school

Multiply everything in the first expression by each thing in the second one and add them together.

(3x +7w +4) (4x - 5w - 2).

(12x^2 + 28xw + 16x)+ (-15xw - 35w^2 - 20w) +(-6x -14xw -8)

I figure you can handle adding the like terms.