(c%2Bd)-simplify.jpeg "(a+b)(c+d) Simplify")
Simplifying (a+b)(c+d)
When working with algebraic expressions, it's often necessary to simplify complex expressions to make them easier to work with. One common expression that requires simplification is (a+b)(c+d). In this article, we'll explore how to simplify this expression and provide a step-by-step guide on how to do it.
The Distributive Property
To simplify (a+b)(c+d), we can use the distributive property of multiplication over addition. This property states that:
a(b+c) = ab + ac
Using this property, we can expand the expression (a+b)(c+d) as follows:
(a+b)(c+d) = ?
Let's start by multiplying the first term (a+b) with the second term (c+d):
a(c+d) = ac + ad
Next, we'll multiply the second term (a+b) with the second term (c+d):
b(c+d) = bc + bd
Now, we'll combine the two expressions:
(a+b)(c+d) = ac + ad + bc + bd
Simplified Expression
The simplified expression for (a+b)(c+d) is:
(a+b)(c+d) = ac + ad + bc + bd
This expression is now in its simplest form, with four terms: ac, ad, bc, and bd.
Example
Let's say we want to simplify the expression (x+2)(y+3). Using the distributive property, we can expand the expression as follows:
(x+2)(y+3) = xy + 3x + 2y + 6
In this example, a=x, b=2, c=y, and d=3. Plugging in these values, we get:
xy + 3x + 2y + 6
This is the simplified expression for (x+2)(y+3).
Conclusion
Simplifying (a+b)(c+d) is a straightforward process that involves applying the distributive property of multiplication over addition. By expanding the expression and combining like terms, we can simplify it to ac + ad + bc + bd. This expression is now in its simplest form, making it easier to work with in various mathematical contexts.
