Question

Simplify
a(a+b-c) + b(a-b+c) = c(-a+b+c)​

Answer 1

How do I simplify the boolean expression of (A+B) •(B+C) •(A+C)?

Let us first define some basic formulas of boolean algebra that we're gonna need for the solution

(X+X)=X

(X.X)=X

(X+1)=1

1.X=X

Now let us get to the problem

(A+B)(B+C)(A+C)

=(AB+AC+BC+BB)(A+C) {Multiplying the first two terms}

=(AB+AC+BC+B)(A+C) {Using formula 2}

=[AB+AC+B(C+1)](A+C) {Taking the common terms}

=(AB+B+AC)(A+C) {Using formulas 3 and 4}

=(AAB+ABC+AB+BC+AAC+ACC)

=(AB+ABC+AB+BC+AC+AC) {Using formula 2}

=(AB+BC+AC+ABC) {Using formula 1}

=[AB+BC+AC+ABC+ABC+ABC] {Using the inverse of formula 1}

=(AB+ABC+BC+ABC+AC+ABC)

=[AB(C+1)+BC(A+1)+AC(B+1)] {Taking the common terms}

=(AB+BC+AC) {Using formulas 3 and 4}

You can keep it in this form or change it a bit more to get

A(B+C)+BC