Answer
Given that: [tex]A = B+Bcd[/tex]
The distributive property says that:
[tex]a \cdot(b+c) = a\cdot b+ a\cdot c[/tex]
Then;
Apply distributive property to the given equation:
[tex]A = B(1+cd)[/tex]
Divide both sides by B we get;
[tex]\frac{A}{B} = 1+cd[/tex]
Subtract 1 from both sides we get;
[tex]\frac{A}{B}-1 = cd[/tex]
Simplify:
[tex]\frac{A-B}{B} = cd[/tex]
Divide both sides by d we get;
[tex]\frac{A-B}{Bd} = c[/tex]
Therefore, the formula for c is :
[tex]c=\frac{A-B}{Bd}[/tex]
