(c-d)%2B(a-b)(c%2Bd)%2B2(ac%2Bbd)-answer.jpeg "(a+b)(c-d)+(a-b)(c+d)+2(ac+bd) Answer")
Expansion of Algebraic Expressions
In algebra, we often come across expressions that involve variables and constants combined using various operations such as addition, subtraction, and multiplication. One such expression is (a+b)(c-d)+(a-b)(c+d)+2(ac+bd). In this article, we will explore how to expand this expression and simplify it to its simplest form.
Expanding the Expression
To expand the given expression, we need to follow the order of operations (PEMDAS) and multiply the binomials.
(a+b)(c-d)
= ac - ad + bc - bd
(a-b)(c+d)
= ac + ad - bc - bd
Adding the Two Expressions
Now, let's add the two expressions we obtained above:
ac - ad + bc - bd + ac + ad - bc - bd
Combining Like Terms
= 2ac - 2bd
Adding 2(ac+bd)
Finally, we add 2(ac+bd) to the expression:
= 2ac - 2bd + 2ac + 2bd
Simplifying the Expression
Combining like terms, we get:
= 4ac
And that's the simplified form of the original expression (a+b)(c-d)+(a-b)(c+d)+2(ac+bd)!
In conclusion, expanding algebraic expressions involves following the order of operations and combining like terms. By doing so, we can simplify complex expressions into their simplest forms.
