(c-d)%2B(a-b)(c%2Bd)%2B2(ac%2Bbd).jpeg "(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)")
Simplifying the Expression: (a+b)(c-d)+(a-b)(c+d)+2(ac+bd)
This article will explore the process of simplifying the algebraic expression: (a+b)(c-d)+(a-b)(c+d)+2(ac+bd). We'll use the distributive property and basic algebraic operations to arrive at a more concise form.
Expanding the Expression
Let's begin by expanding the expression using the distributive property:
- (a+b)(c-d) = ac - ad + bc - bd
- (a-b)(c+d) = ac + ad - bc - bd
Substituting these expansions into the original expression, we get:
(ac - ad + bc - bd) + (ac + ad - bc - bd) + 2(ac + bd)
Combining Like Terms
Now, let's combine the like terms:
- ac + ac + 2ac = 4ac
- -ad + ad = 0
- bc - bc = 0
- -bd - bd + 2bd = 0
Simplified Expression
Finally, we have simplified the expression to:
(a+b)(c-d)+(a-b)(c+d)+2(ac+bd) = 4ac
Therefore, the simplified form of the given expression is 4ac.