Problem: Generating an expression that removes the parentheses using first principles.

Given (a+b)(c+d) = ab+ac+bc+bd,

Can we say: (a+b)÷(c+d) = a/c+a/d+b/c+b/d is True? (no we can't if we use test data!)

What I really want is to express R, so far I know R = (360 over W) - 10 - (R.(T -75W) over W)

So I'm trying to isolate for R on LHS only.

Workings:

If a=b=1 and c=d=2 then

For (a+b)(c+d),

≍ (1+1)÷(2+2)

≍ 2÷4 = 1/2

For a/c+a/d+b/c+b/d,

≍ 1/2 + 1/2 + 1/2 + 1/2 = 2 So no it's not true, but invert 2 and it's 1/2 are we close,

can we say:

(a+b)(c+d) = _________1_________

a/c+a/d+b/c+b/d

Where a=1, b=4, c=2, d=8

Testing (a+b)(c+d) = (1+4)(2+8)

=(5)(10) =50

Testing _________1_________ = _________1_________

a/c+a/d+b/c+b/d 1/2+1/8+4/2+4/8

= _________1__________

4/8+1/8+16/8+4/8

= ___1___

25/8

=8/25 ≠ 50 So no that's not it!

Please help me. The actual equation I'm trying to simply for programming purposes is:

R = (360 over W) - 10 - (R.(T -75W) over W)

I need to express the equation isolating R on one side of equation only.