(c-d)%2B(a-b)(c%2Bd)%2B2(ac%2Bbd)-solution.jpeg "(a+b)(c-d)+(a-b)(c+d)+2(ac+bd) Solution")
Solving the Algebraic Expression: (a+b)(c-d)+(a-b)(c+d)+2(ac+bd)
In this article, we will solve the algebraic expression (a+b)(c-d)+(a-b)(c+d)+2(ac+bd). This expression involves the use of parentheses, addition, subtraction, and multiplication of algebraic terms.
Step 1: Evaluate the Expressions inside the Parentheses
First, let's evaluate the expressions inside the parentheses:
(a+b)(c-d) = a(c-d) + b(c-d) = ac - ad + bc - bd
(a-b)(c+d) = a(c+d) - b(c+d) = ac + ad - bc - bd
Step 2: Simplify the Expressions
Now, let's simplify the expressions:
ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd
Step 3: Combine Like Terms
Next, let's combine like terms:
2ac - 2bd + 2ac + 2bd = 4ac
The final expression is 4ac.
Conclusion
Therefore, the solution to the algebraic expression (a+b)(c-d)+(a-b)(c+d)+2(ac+bd) is 4ac. This expression can be simplified to a single term by combining like terms.
